• Afanasyev, Y. D., and W. R. Peltier, 1998: The three-dimensionalization of stratified flow over two-dimensional topography. J. Atmos. Sci.,55, 19–39.

  • Andreassen, O., C. E. Wasberg, D. C. Fritts, and J. R. Isler, 1994: Gravity wave breaking in two and three dimensions. 1. Model description and comparison of two-dimensional evolutions. J. Geophys. Res.,99 (D), 8095–8108.

  • Armi, L., and R. Williams, 1993: The hydraulics of a stratified fluid flowing through a contraction. J. Fluid Mech.,251, 355–375.

  • Benjamin, S. G., K. J. Brundage, and L. L. Morone, 1994: The rapid update cycle. Part 1: Analysis/model description. Tech. Procedures Bull. 416, 16 pp. [Available from NOAA/NWS, Mary Howell, 13205 W/OM21 SSMC #2, 1325 East–West Highway, Silver Spring, MD 20910.].

  • Bennetts, D. A., and B. J. Hoskins, 1979: Conditional symmetric instability—A possible explanation for frontal rainbands. Quart. J. Roy. Meteor. Soc.,105, 945–962.

  • Bernard, A., D. Demaiffe, N. Mattielli, and R. S. Punongbayan, 1991:Anhydrite-bearing pumices from Mount Pinatubo: Further evidence for the existence of sulphur-rich silicic magmas. Nature,354, 139–140.

  • Brinkmann, W. A. R., 1974: Strong downslope winds at Boulder, Colorado. Mon. Wea. Rev.,102, 592–602.

  • Browand, F. K., and C. D. Winant, 1973: Laboratory observations of shear-layer instability in a stratified fluid. Bound.-Layer Meteor.,5, 67–77.

  • Caulfield, C. P., 1994: Multiple linear instability of layered stratified shear flow. J. Fluid Mech.,258, 255–285.

  • Clark, T. L., 1977: A small scale numerical model using a terrain following coordinate transformation. J. Comput. Phys.,24, 186–215.

  • ——, and W. R. Peltier, 1977: On the evolution and stability of finite-amplitude mountain waves. J. Atmos. Sci.,34, 1715–1730.

  • ——, and W. R. Farley, 1984: Severe downslope windstorm calculations in two and three spatial dimensions using anelastic interactive grid nesting: A possible mechanism for gustiness. J. Atmos. Sci.,41, 329–350.

  • ——, and W. D. Hall, 1991: Multi-domain simulations of the time dependent Navier Stokes equations: Benchmark error analyses of some nesting procedures. J. Comput. Phys.,92, 456–481.

  • ——, and ——, 1996: The design of smooth, conservative vertical grids for interactive grid nesting with stretching. J. Appl. Meteor.,35, 1040–1046.

  • ——, ——, and R. M. Banta, 1994: Two-and three-dimensional simulations of the 9 Jan 1989 severe Boulder windstorm: Comparison with observations. J. Atmos. Sci.,51, 2317–2343.

  • ——, T. Keller, J. Coen, P. Neilley, H.-M. Hsu, and W. D. Hall, 1997:Terrain-induced turbulence over Lantau Island: 7 June 1994 Tropical Storm Russ case study. J. Atmos. Sci.,54, 1795–1814.

  • Durran, D. R., 1995: Do breaking mountain waves decelerate the local mean flow? J. Atmos. Sci.,52, 4010–4032.

  • FAA, 1985: Federal aviation regulations. Part 25—Airworthiness standards, transport category airplanes. Federal Aviation Administration, 112 pp. Available from Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402.

  • Fritts, D. C., and Z. Luo, 1992: Gravity wave excitation by geostrophic adjustment of the jet stream. Part I: Two-dimensional forcing. J. Atmos. Sci.,49, 681–697.

  • ——, J. R. Isler, and O. Andreassen, 1994: Gravity wave breaking in two and three dimensions. 2. Three-dimensional evolution and instability structure. J. Geophys. Res.,99 (D), 8109–8023.

  • Hamming, R. W., 1983: Digital Filters. Prentice-Hall, 257 pp.

  • Holmboe, J., 1962: On the behavior of symmetric waves in stratified shear layers. Geofys. Publ.,24, 67–61.

  • Isler, J. R., D. C. Fritts, O. Andreassen, and C. E. Wasberg, 1994: Gravity wave breaking in two and three dimensions. 3. Vortex breakdown and transition to isotropy. J. Geophys. Res.,99 (D4), 8125–8137.

  • Jones, S., and A. J. Thorpe, 1992: The three-dimensional nature of“symmetric” instability. Quart. J. Roy. Meteor. Soc.,118, 227–258.

  • Kerr, R. M., J. A. Domaradzki, and G. Barbier, 1996: Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence. Phys. Fluids,8, 197–208.

  • Klaassen, G. P., and W. R. Peltier, 1989: The role of transverse secondary instabilities in the evolution of free shear layers. J. Fluid Mech.,202, 367–402.

  • Klemp, J. B., and D. K. Lilly, 1978: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci.,35, 78–107.

  • Koscielny, A. J., R. J. Doviak, and R. Rabin, 1982: Statistical considerations in the estimation of divergence from a single Doppler radar and application to prestorm boundary-layer observations. J. Appl. Meteor.,21, 197–210.

  • Ley, B. E., and W. R. Peltier, 1978: Wave generation and frontal collapse. J. Atmos. Sci.,35, 3–17.

  • Lilly, D. K., and E. J. Zipser, 1972: The front range windstorm of 11 January 1972: A meteorological narrative. Weatherwise,25, 56–63.

  • ——, and P. J. Kennedy, 1973: Observations of a stationary mountain wave and its associated momentum flux and energy dissipation. J. Atmos. Sci.,30, 1135–1152.

  • ——, J. M. Nicholls, R. M. Chervin, P. J. Kennedy, and J. B. Klemp, 1982: Aircraft measurements of wave momentum flux over the Colorado Rocky Mountains. Quart. J. Roy. Meteor. Soc.,108, 625–642.

  • May, P. T., K. P. Moran, and R. G. Strauch, 1989: The accuracy of RASS temperature profiles. J. Appl. Meteor.,28, 1329–1335.

  • McCormick, B. W., 1995: Aerodynamics, Aeronautics, and Flight Mechanics. 2d ed. John Wiley and Sons, 652 pp.

  • Moran, K. P., and R. G. Strauch, 1994: The accuracy of RASS temperature measurements corrected for vertical air motions. J. Atmos. Oceanic Technol.,11, 995–1001.

  • Neiman, P. J., R. M. Hardesty, M. A. Shapiro, and R. E. Cupp, 1988:Doppler lidar observations of a downslope windstorm. Mon. Wea. Rev.,116, 2265–2275.

  • ——, P. T. May, and M. A. Shapiro, 1992: Radio Acoustic Sounding System (RASS) and wind profiler observations of lower and midtropospheric weather systems. Mon. Wea. Rev.,120, 2298–2313.

  • O’Sullivan, D., and T. J. Dunkerton, 1995: Generation of inertia–gravity waves in a simulated life cycle of baroclinic instability. J. Atmos. Sci.,52, 3695–3716.

  • Peltier, W. R., and T. L. Clark, 1979: The evolution and stability of finite amplitude mountain waves—II: Mountain wave drag and severe downslope windstorms. J. Atmos. Sci.,36, 1499–1529.

  • ——, and ——, 1983: Non-linear mountain waves in two and three spatial dimensions. Quart. J. Roy. Meteor. Soc.,109, 527–548.

  • Pierrehumbert, R. T., and B. Wyman, 1985: Upstream effects of mesoscale mountains. J. Atmos. Sci.,42, 977–1003.

  • Post, M. J., and R. E. Cupp, 1990: Optimizing a pulsed Doppler lidar. Appl. Opt.,29, 4145–4158.

  • ——, A. Weickmann, K. R. Healy, R. J. Willis, and C. Grund, 1996:Comparison of Mount Pinatubo and El Chichon volcanic events:Lidar observations at 10.6 and 0.69 μm. J. Geophys. Res.,101, 3929–3940.

  • Ralph, F. M., M. Crochet, and S. V. Venkateswaran, 1992: A study of mountain lee waves using clear-air radar. Quart. J. Roy. Meteor. Soc.,118, 597–627.

  • ——, P. J. Neiman, and D. Levinson, 1997: Lidar observations of a breaking mountain wave associated with extreme turbulence. Geophys. Res. Lett.,24, 663–666.

  • Rayleigh, Lord, 1880: On the stability and instability of certain fluid motions. Proc. London. Math. Soc.,11, 57–75.

  • Richard, E., P. Mascart, and E. C. Nickerson, 1989: The role of surface friction in downslope windstorms. J. Appl. Meteor.,28, 241–251.

  • Rottman, J. W., and R. B. Smith, 1989: A laboratory model of severe downslope winds. Tellus,41A, 401–415.

  • Schwartz, B., 1996: The quantitative use of PIREPS in developing aviation weather guidance products. Wea. Forecasting,11, 372–384.

  • Silvers, C. L., and C. C. Withers, 1975: Evaluation of the flying qualities requirements of MIL-F-8785B. Air Force Flight Dynamics Lab Rep. AFFDL-TR-75-3, 333 pp. NTIS AD-A011 728/3/XAB.

  • Smith, R. B., 1976: The generation of lee waves by the Blue Ridge. J. Atmos Sci.,33, 507–519.

  • ——, 1987: Aerial observations of the Yugoslavian Bora. J. Atmos. Sci.,44, 269–297.

  • Smyth, W. D., G. P. Klaassen, and W. R. Peltier, 1988: Finite amplitude Holmboe waves. Geophys. Astrophys. Fluid Dyn.,43, 181–222.

  • van Tuyl, A. H., and J. A. Young, 1982: Numerical simulation of nonlinear jet streak adjustment. Mon. Wea. Rev.,110, 2038–2054.

  • View in gallery

    A 300-mb analysis of geopotential height (bold solid) and wind speed (m s−1, thin solid; shading: 40–50 and 60–70 m s−1) at (a) 1200 UTC 9 Dec 1992 and (b) 0000 UTC 10 Dec 1992. The 300-mb wind vector flags are 25 m s−1, full barbs are 10 m s−1, and half-barbs are 2.5 m s−1. Wind vectors with solid-dot heads are wind profiler observations, without heads are rawinsonde observations, and stand-alone solid dots are rawinsonde thermodynamic observations.

  • View in gallery

    Time–height section of hourly averaged wind profiles and total wind speed (m s−1, thin solid) observed by the 404-MHz wind profiler at Platteville, CO, between 0530 and 2230 UTC 9 Dec 1992. (a) Every other range gate is shown. Wind flags and barbs, and isotach shading are as in Fig. 1. The dashed lines represent the intermediate 35 m s−1 isotach. (b) A simulated profile from domain 3 between 1000 and 1700 UTC. The heavy dashed lines in (a) denote the boundaries of (b).

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    Hourly averaged profiler wind (m s−1) and RASS potential temperature (K) θυ data between 2330 UTC 8 Dec and 2330 UTC 9 Dec 1992. Wind speed shown in bold gray shade and westerly component as dashed. Winds taken from the 404-MHz Platteville profiler. Here, θυ is shown as thin solid with regions of poor RASS coverage shown as dashed. Data taken from the 50-MHz Platteville above 3 km MSL and from the 915-MHz Erie, CO, profiler/RASS systems below 3 km MSL. Hourly averaged surface winds measured at Boulder are included. Wind flags and barbs are as in Fig. 1.

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    Skew-T, logp plot of temperature and dewpoint temperature (°C) from the Denver, CO, rawinsonde ascents. The companion wind profiles are also shown. Wind flags and barbs are as in Fig. 1.

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    Vertically stacked w time series from the 404-MHz wind profiler at Platteville, CO, between 0600 and 2300 UTC 9 Dec 1992 (scale lower right). The data were smoothed using a single pass of a temporal Hann filter. Every other range gate is shown. Approximately six data points were deemed “bad” and subjectively edited. Those bad points (approximately one-half), which were surrounded by good data, were given new values determined by linear temporal interpolation. The shaded area between 10 and 11 km marks the approximate position of the tropopause. The bold dot marks the aircraft incident.

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    (a) Backscattered power measured by the Doppler lidar in a west–east RHI at 1605 UTC 9 Dec 1992. Radial velocity (Vr, m s−1) is shown in (b) as color-contoured raw data, (c) as line-contoured data. (d) An RHI of radial velocities derived from the simulated winds at the same time and positions as in (c). Negative (positive) values are toward (away from) the lidar. The scan took 60 s using a scan rate of 3° s−1. Three-

  • View in gallery

    (Continued) pulse averaging was used to calculate Vr at 3 Hz. The pulse volume is 300 m long and 0.9 m wide at 10 km range and is shown for reference. Lenticular clouds and the tropopause are also shown in (c) based on the distribution of backscattered power in (a). The tropopause in (d) is derived using θ data. The smoothed mountain profile is shown in gray. From Ralph et al. (1997).

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    (a) Backscattered power measured by the Doppler lidar in SSW–NNE (210°–30°) RHI scan at 1552 UTC 9 Dec 1992. Radial velocity (Vr, m s−1) is shown in (b) as color-contoured raw data and (c) as line-contoured data. Negative (positive) values are toward (away from) the lidar. The tropopause, based on backscatter power measurements, is marked by the solid line.

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    (a) Schematic showing a geometric interpretation of the HVT and (b) disturbed tropopause surface in Fig. 7.

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    Defense Meteorological Satellite image taken of eastern Colorado at 1506 UTC Dec 1992. The white + indicates the location of the aircraft incident and the black • indicates the lidar position.

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    Base map and pilot reports for 9 Dec 1992. (a) Base map of northeastern Colorado showing terrain contours (500-m intervals;darkest shading is >3500 m MSL), instrument locations (P, E, and S, represent Platteville, Erie, and Stapleton wind profiler/RASS locations), pilot reports of turbulence (see legend for intensity), and the location of an aircraft accident at 1510 UTC.

  • View in gallery

    (Continued) (b) Cross-mountain cross section showing the positions of pilot turbulence reports (see legend for intensity) between 39.5° and 40.3°N. Labeled times are to the nearest hour (UTC). Dots mark the precise locations of the turbulence reports, when available, and “several” refers to several reports in that vicinity. The positions of the lidar-observed tropopause and flow reversal at 1600 UTC are shown, as are the positions of the aircraft accident at 1510 UTC, the Doppler lidar, and the Platteville wind profiler.

  • View in gallery

    Topography of the outermost domain with the outline of the four inner domains. The thin outline shows the state boundaries of Colorado. Contour interval is 250 m. BOU, DEN, GJT, and CSP refer to Boulder, Denver, Grand Junction, and Colorado Springs, respectively.

  • View in gallery

    Time sequence of the 10-min average 〈θ〉 at 4659 m MSL from the fourth domain (400 m × 400 m grids). The thick solid lines show the underlying topography (250-m interval). Temperatures shown range between 288.52 and 293.91 K. The locations of the lidar and the aircraft incident are marked with Xs.

  • View in gallery

    Temporally averaged fields from the fifth domain at 6287 m MSL at 1410 UTC. Averaging period is 30 min. Shown are (a) streamwise flow 〈us〉, (b) cross-stream flow 〈un〉, (c) vertical velocity 〈w〉, and (d) potential temperature 〈θ〉. The streamwise direction was defined as WNW 288°. The solid lines show the underlying topography (250-m interval). Vectors show nonaveraged horizontal winds.

  • View in gallery

    Same as Fig. 13 except at 11 583 m MSL. The streamwise direction was defined as WNW 315°. Vectors show nonaveraged horizontal winds.

  • View in gallery

    Streamwise velocity 〈us〉 at 1415 UTC on four vertical cross-stream planes oriented normal to 288°. Horizontal scale shown is for y axis, whereas actual distances are 1.05 times larger. Isentropes are shown as broken contours and velocities are shown using a grayscale.

  • View in gallery

    Streamwise velocity 〈us〉 at 1415 UTC on four vertical cross-stream planes oriented normal to 315°. Horizontal scale shown is for y axis, whereas actual distances are 1.41 times larger. Isentropes are shown as broken contours.

  • View in gallery

    Three-dimensional perspectives of the simulated flow at 1415 UTC with the viewer looking toward the northwest. Each figure shows the isosurface of u = 55 m s−1 in light gray. The black isosurfaces show (a) |ω| = 0.20 s−1; (b) the buoyancy production term for |ω|, (gωxByωyBx)1/3 = 0.026s−1, where Bx and By are the x and y derivatives of buoyancy; and (c) the stretching production term for |ω|, (ωieijωj)1/3 = 0.03 s−1, where ω = × u and eij = (∂ui/∂xj + ∂uj/∂xi)/2.

  • View in gallery

    Time sequence of the perturbation vertical velocity, w′, at 6287 m MSL from the fifth domain.

  • View in gallery

    Three-dimensional rendering of jet stream and σq. The red shows the surface of u = 55 m s−1 and the yellow shows the surface of σq = 10 m s−1. Arrows point to sources of CAT discussed in text.

  • View in gallery

    Time sequence of σq at 1066 m AGL. Thick dark contours show orography in increments of 250 m.

  • View in gallery

    Total vertical velocity, w, on four vertical cross-stream planes at 1415 UTC. Horizontal scale shown is for y axis, whereas actual distances are 1.05 times larger.

  • View in gallery

    Cross-stream or spanwise velocity un on four cross-stream planes at 1415 UTC. The streamwise direction was defined as WNW 288°. Horizontal scale shown is for y axis, whereas actual distances are 1.05 times larger.

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Origins of Aircraft-Damaging Clear-Air Turbulence during the 9 December 1992 Colorado Downslope Windstorm: Numerical Simulations and Comparison with Observations

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  • 1 National Center for Atmospheric Research*, Boulder, Colorado
  • | 2 NOAA/ERL/Environmental Technology Laboratory, Boulder, Colorado
  • | 3 CIRES, University of Colorado/NOAA, Boulder, Colorado
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Abstract

Results from numerical simulations of the Colorado Front Range downslope windstorm of 9 December 1992 are presented. Although this case was not characterized by severe surface winds, the event caused extreme clear-air turbulence (CAT) aloft, as indicated by the severe structural damage experienced by a DC-8 cargo jet at 9.7 km above mean sea level over the mountains. Detailed measurements from the National Oceanic and Atmospheric Administration/Environmental Research Laboratories/Environmental Technology Laboratory Doppler lidar and wind profilers operating on that day and from the Defense Meteorological Satellite Program satellite allow for a uniquely rich comparison between the simulations and observations.

Four levels of grid refinement were used in the model. The outer domain used National Centers for Environmental Prediction data for initial and boundary conditions. The finest grid used 200 m in all three dimensions over a 48 km by 48 km section. The range of resolution and domain coverage were sufficient to resolve the abundant variety of dynamics associated with a time-evolving windstorm forced during a frontal passage. This full range of resolution and model complexity was essential in this case. Many aspects of this windstorm are inherently three-dimensional and are not represented in idealized models using either 2D or so-called 2D–3D dynamics.

Both the timing and location of wave breaking compared well with observations. The model also reproduced cross-stream wavelike perturbations in the jet stream that compared well with the orientation and spacing of cloud bands observed by satellite and lidar. Model results also show that the observed CAT derives from interactions between these wavelike jet stream disturbances and mountain-forced internal gravity waves. Due to the nearly east–west orientation of the jet stream, these two interacting wave modes were orthogonal to each other. Thermal gradients associated with the intense jet stream undulations generated horizontal vortex tubes (HVTs) aligned with the mean flow. These HVTs remained aloft while they propagated downstream at about the elevation of the aircraft incident, and evidence for such a vortex was seen by the lidar. The model and observations suggest that one of these intense vortices may have caused the aircraft incident.

Reports of strong surface gusts were intermittent along the Front Range during the period of this study. The model showed that interactions between the gravity waves and flow-aligned jet stream undulations result in isolated occurrences of strong surface gusts in line with observations. The simulations show that strong shears on the upper and bottom surfaces of the jet stream combine to provide an episodic “downburst of turbulence.” In the present case, the perturbations of the jet stream provide a funnel-shaped shear zone aligned with the mean flow that acts as a guide for the downward transport of turbulence resulting from breaking gravity waves. The physical picture for the upper levels is similar to the surface gusts described by Clark and Farley resulting from vortex tilting. The CAT feeding into this funnel came from all surfaces of the jet stream with more than half originating from the vertically inclined shear zones on the bottom side of the jet stream. Visually the downburst of turbulence looks similar to a rain shaft plummeting to the surface and propagating out over the plains leaving relatively quiescent conditions behind.

Corresponding author address: Dr. Terry L. Clark, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000.

Email: clark@ncar.ucar.edu

Abstract

Results from numerical simulations of the Colorado Front Range downslope windstorm of 9 December 1992 are presented. Although this case was not characterized by severe surface winds, the event caused extreme clear-air turbulence (CAT) aloft, as indicated by the severe structural damage experienced by a DC-8 cargo jet at 9.7 km above mean sea level over the mountains. Detailed measurements from the National Oceanic and Atmospheric Administration/Environmental Research Laboratories/Environmental Technology Laboratory Doppler lidar and wind profilers operating on that day and from the Defense Meteorological Satellite Program satellite allow for a uniquely rich comparison between the simulations and observations.

Four levels of grid refinement were used in the model. The outer domain used National Centers for Environmental Prediction data for initial and boundary conditions. The finest grid used 200 m in all three dimensions over a 48 km by 48 km section. The range of resolution and domain coverage were sufficient to resolve the abundant variety of dynamics associated with a time-evolving windstorm forced during a frontal passage. This full range of resolution and model complexity was essential in this case. Many aspects of this windstorm are inherently three-dimensional and are not represented in idealized models using either 2D or so-called 2D–3D dynamics.

Both the timing and location of wave breaking compared well with observations. The model also reproduced cross-stream wavelike perturbations in the jet stream that compared well with the orientation and spacing of cloud bands observed by satellite and lidar. Model results also show that the observed CAT derives from interactions between these wavelike jet stream disturbances and mountain-forced internal gravity waves. Due to the nearly east–west orientation of the jet stream, these two interacting wave modes were orthogonal to each other. Thermal gradients associated with the intense jet stream undulations generated horizontal vortex tubes (HVTs) aligned with the mean flow. These HVTs remained aloft while they propagated downstream at about the elevation of the aircraft incident, and evidence for such a vortex was seen by the lidar. The model and observations suggest that one of these intense vortices may have caused the aircraft incident.

Reports of strong surface gusts were intermittent along the Front Range during the period of this study. The model showed that interactions between the gravity waves and flow-aligned jet stream undulations result in isolated occurrences of strong surface gusts in line with observations. The simulations show that strong shears on the upper and bottom surfaces of the jet stream combine to provide an episodic “downburst of turbulence.” In the present case, the perturbations of the jet stream provide a funnel-shaped shear zone aligned with the mean flow that acts as a guide for the downward transport of turbulence resulting from breaking gravity waves. The physical picture for the upper levels is similar to the surface gusts described by Clark and Farley resulting from vortex tilting. The CAT feeding into this funnel came from all surfaces of the jet stream with more than half originating from the vertically inclined shear zones on the bottom side of the jet stream. Visually the downburst of turbulence looks similar to a rain shaft plummeting to the surface and propagating out over the plains leaving relatively quiescent conditions behind.

Corresponding author address: Dr. Terry L. Clark, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000.

Email: clark@ncar.ucar.edu

1. Introduction

In situ aircraft observations of windstorms (Lilly and Zipser 1972; Lilly and Kennedy 1973; Lilly et al. 1982;Smith 1976, 1987) have significantly advanced our knowledge of windstorm flow structures and continue to inspire theoretical studies that improve our understanding of windstorm dynamics. These observations are severely limited by the constraints of mapping complex flows using only in situ measurements of winds, temperature, and turbulence characteristics. As a result, many of the derived fields required considerable interpolation and interpretation. More recently, remote sensing using the ground-based lidar of National Oceanic and Atmospheric Administration/Environmental Research Laboratories/Environmental Technology Laboratory (NOAA/ERL/ETL) has significantly improved the observations of such flow fields (Neiman et al. 1988;Ralph et al. 1992; Ralph et al. 1997). Ralph et al. (1997) observed elevated regions of breaking internal gravity waves excited by flow over the Front Range near Boulder, Colorado. The recent observations of the 9 December 1992 windstorm are sufficiently detailed to allow comparison of model results with observations to test our theoretical understanding of windstorm dynamics. Surface winds peaked at ≈35 m s−1 in Boulder at 1300–1315 UTC, indicating that it was strong enough to be in the Brinkmann (1974) categories used to study the climatology of Boulder windstorms but weaker than the strongest events, which can exceed 50 m s−1. Although the surface winds were not extreme, numerous pilot reports of severe clear-air turbulence (CAT) were received. The severity of the CAT during the windstorm on 9 December 1992 was attested to by an aircraft incident when a DC-8 cargo plane had 19 ft of a wing plus one of its four engines torn off at the cruising elevation of 9.7 km above mean sea level (MSL) during an attempted westward passage over the Front Range. A photo of the damaged jet appears in Ralph et al. (1997). At the time of the aircraft incident a visible image from a polar-orbiting Defense Meteorological Satellite Program (DMSP) satellite revealed a foehn gap east of the Continental Divide along with high-elevation banded clouds aligned with the mean northwesterly flow that appear to emanate from overhead and downwind of the foehn gap. This paper presents observational and numerical results from a case study of the 9 December 1992 windstorm. The comparison of model results with lidar and satellite observations corroborates our findings and shows that this particular windstorm departs considerably from the conventional two-dimensional picture of windstorm dynamics where the dynamics is driven by the effects of breaking internal gravity waves.

Early theoretical studies of windstorms focused on the two-dimensional hydrostatic dynamics associated with stable air flowing over large-scale mountains. Early studies included those of Clark and Peltier (1977), Klemp and Lilly (1978), and Peltier and Clark (1979, 1983) where the main focus was on understanding mechanisms leading to the strong amplification observed in these flows that could not be explained with linear theory. Self-induced resonance, provided by the super-adiabatic wave-breaking region, was first suggested by Peltier and Clark (1979) and has become recognized as an important factor in the dynamics of severe downslope windstorms. However, what is not well resolved is the comprehensiveness of this essentially two-dimensional theory in explaining the dynamics resulting in flows where a broad range of forcing is provided by the baroclinic structures associated with frontal passage.

Numerical and laboratory (e.g., Rottman and Smith 1989) experiments studying windstorm dynamics have been typically idealized to the point where strong three-dimensional effects are ignored. This idealization can be rationalized as realistic provided that the mean flow normal to the ridge is approximately in balance with an upstream horizontally uniform forcing. In such cases, variations in the along-ridge mean flow can be neglected. The observations and modeling analyses of the 9 December 1992 windstorm show that this assumption was invalid on that occasion and that the dynamics associated both with wave breaking and with frontal forcing are essential in explaining the onset and character of the windstorm.

Theoretical studies focusing on the three-dimensional dynamics of windstorms include Clark and Farley (1984), Clark et al. (1994), and Afanasyev and Peltier (1998). Clark and Farley (1984) extended the Peltier and Clark (1979) study of the 11 January 1972 Boulder windstorm to three dimensions by including a north–south ridge. The limited area domain in the north–south direction was sufficient to identify the tilting of horizontal vortices within the wave-breaking region, which subsequently plunged to the surface causing severe surface gusts. Similar so-called 2D–3D experiments, by Afanasyev and Peltier (1998), used increased resolution over Clark and Farley to investigate cross-roll instabilities. Both these studies used bell-shaped orography and free-slip lower boundary conditions, and Coriolis was treated using an f-plane approximation in Clark and Farley (1984). An important effect of Coriolis is that it limits the upstream extent of blocking, which can be fundamental to a realistic representation of upstream boundary conditions (Pierrehumbert and Wyman 1985). Clark et al. (1994) extended the three-dimensional simulations to include realistic topography and surface friction using a drag law formulation. Coriolis was again treated using an f-plane approximation. They idealized the large-scale forcing by assuming horizontally uniform and steady-state upstream conditions. A number of sources of surface gustiness were identified including vortex tilting from within the wave-breaking region leading to the most intense surface gusts. The present study relaxes these idealizations and uses fully time-dependent boundary conditions derived from the forcing by large-scale data of the National Centers for Environmental Prediction. Surface friction is again considered using a drag law formulation, but the near-surface horizontal resolutions are inadequate to resolve the adverse pressure gradient required to capture flow separation. Adequate vertical resolution is relatively easy to attain in these studies using vertical grid stretching. The highest horizontal resolution used in this study is a 200-m grid, whereas Clark et al. (1997) required approximately 60-m horizontal grid spacing to capture flow separation at the surface in a case dominated by mechanical turbulence. The extreme computational cost plus the fact that flow separation at the surface may be suppressed by internal gravity wave downdrafts has led researchers to ignore effects of mechanical turbulence in hydrostatic-scale flows such as this. However, some important large-scale effects of surface friction (Richard et al. 1989; Clark et al. 1994) are captured. A full generalization certainly allows one to treat windstorms realistically and perform case studies, but the lack of idealizations makes it difficult to perform sensitivity studies to extract the important governing dynamics. On the other hand, such case studies are general enough that they provide the insight necessary to help define future idealizations and sensitivity studies necessary to better understand realistic flows. There are still a number of outstanding questions that remain from this study requiring further investigation.

Elevated wave breaking can lead to an effective reflector of both hydrostatic and nonhydrostatic vertically propagating gravity waves with subsequent amplification through constructive interference. Most idealized studies show this type of reflection leading to a dramatic lowering of the wave-breaking region, while the flow between the super-adiabatic region and the surface accelerates and wave drag increases. However, such flow evolution is not always readily apparent in some of the more realistic case studies (Lilly and Kennedy 1973; Durran 1995). Details in both the vertical and horizontal structure of the larger-scale flow are important in determining the nature of the evolution. The vertical structures are important in defining the characteristics of the medium supporting vertical wave propagation, whereas horizontal variability affects the nature of both the upstream and downstream boundary conditions. Horizontal structure is also important in determining the role of gravity–inertia waves and is essential in representing frontal dynamics. The present case of 9 December 1992 is one with a strong jet centered near 9 km MSL with wave breaking occurring well into the stratosphere between 11 and 13 km MSL. There was little, if any, lowering of the super-adiabatic region for this case, and the flows below and above the jet stream maximum appear to be relatively independent of one another. The type of flow regime might be compared to mode four in the tank experiments of Armi and Williams (1993) where they maintained upper and lower flow separation by providing two downstream vertically separated outflow vents. A possible cause of this type of two-level flow regime, in the present case, is that wave breaking occurred rather high in the stratosphere with the effect that deep vertical penetration requires strong forcing to overcome the negative buoyancy involved in bringing such potentially warm stratospheric air to the surface. The source regions for CAT are not confined to the vicinity of the wave-breaking region nor to shear layers resulting from wave breaking but occur throughout the troposphere. Most CAT in the present case appears to result from shearing instabilities over the entire convoluted surface of the jet stream where some of these shear zones are nearly vertically oriented. There is some indication of flow-aligned vortex pairs within the wave-breaking region, which are presumably a result of the cross-roll instabilities (Klaassen and Peltier 1989; Afanasyev and Peltier 1998; Andreassen et al. 1994; Fritts et al. 1994; Isler et al. 1994); however, these appear to play a relatively minor role in the CAT of this particular case.

The current observation and modeling study of 9 December 1992 show that interactions between the conventional two-dimensional internal breaking gravity wave dynamics and baroclinic processes associated with the frontal passage are fundamental to the dynamics. As a result of these interactions, this particular windstorm is one where severe turbulence mostly remained aloft with only intermittent reports of strong surface gusts. Two types of coherent structures associated with CAT will be presented in this paper. The first is what we term a “downburst of turbulence” resulting from interactions between flow-aligned waves associated with the frontal system. This downburst of turbulence has some strong similarities to the vortex tilting gusts first identified by Clark and Farley (1984). The second type of CAT are flow-aligned linear structures resulting from shearing instabilities along the surface of the highly distorted jet stream. We will show one example of these linear structures forming what we term horizontal vortex tubes (HVTs) occurring at the same elevation as the aircraft incident.

The intermittent downburst of turbulence as well as the CAT flow-aligned linear structures require an understanding of the cause of the jet stream undulations aligned with the upper-level east–west-oriented frontal system. Since the cause of these undulations (or waves) is still unresolved in the literature, we intend to present primarily the morphology of the mean and turbulent flows. The horizontal scale of the flow-aligned jet stream undulations is about 14 km with the disturbances extending between 2 and 3 km in the vertical. Clusters of flow-aligned vortices occurred within the depressed regions of the jet stream. The present windstorm occurs in the exit region of the jet stream. We believe that the origin of the 14-km cross-stream jet stream undulations results from a fundamental instability in the flow and that topography acts only to modulate the local position and strength of the instability. Possible mechanisms for both the 14-km cross-flow scale and smaller-scale flow-aligned vortices will be discussed.

The paper is organized as follows. First, the observations associated with large-scale synoptic weather conditions, radar wind profilers, surface mesonetwork observing sites, and small-scale lidar measurements will be summarized. Second, the numerical model will be described, including the details of domains used, boundary conditions, and initializations. The numerical results are then presented, followed by a discussion of the cross-flow waves and conclusions.

The dynamic three-dimensional flow-modeling analysis that lies at the heart of this work is difficult to display using static two-dimensional views. As a means of improving the readers’ appreciation of the simulated results, we offer three-dimensional animated perspectives of many of our figures on our Web site (http://box.mmm.ucar.edu: 80/csm/windstorm/windstorm.html).

2. Observations

a. Synoptic weather conditions

On 9 December 1992 the synoptic-scale conditions over Colorado were dominated by northwesterly flow, a lower to midlevel tropospheric frontal zone crossing the Rocky Mountains, and the approach of an upper-tropospheric 75 m s−1 jet–front system from the northwest (Fig. 1). Maximum wind speeds were located between 250 and 300 mb (9.5–10.5 km MSL). Winds at this level increased over northeastern Colorado from 28 m s−1 at 0600 UTC to 69 m s−1 at 0000 UTC 10 December, as seen in hourly wind profiler measurements (Fig. 2a). Figure 2b shows a model comparison between 1000 and 1700 UTC on 9 December 1902. The result of using the NOAA Mesoscale Analysis and Prediction System (MAPS) for initialization and boundary conditions is that the simulated jet stream is about 1 km lower than the observed and slightly delayed. Other than that, the comparison in jet stream structure is close to the observed. Continuous vertical profiling of virtual temperature using radio acoustic sounding systems (RASSs) (e.g., Neiman et al. 1992; May et al. 1989; Moran and Strauch 1994) shows a midtropospheric layer of strong stratification from 6 to 4 km MSL that descends between 0000 and 1500 UTC 9 December (Fig. 3). Over the same time period at an altitude near the height of the Continental Divide (4 km MSL), the westerly wind component increased from <10 m s−1 to 25 m s−1. By 1500 UTC the shear between 3 and 7 km MSL was very weak [<5 m s−1 (4 km)−1].

A weak cold front in the lower and midtroposphere moved southeast across Colorado on 9 December 1992. As is common for weak frontal systems approaching Colorado from the northwest, its manifestation at the surface was not well defined, perhaps due to the masking effects of the mountains. However, it was clearly present above 700 mb in rawinsonde data from Colorado, Wyoming, Utah, and Idaho. The weak frontal zone did not include a strong wind direction shift, but it was marked by a 2° to 3°C cooling at 700 mb at these sites between 1200 UTC 9 December and 0000 UTC 10 December. The maximum cooling at Denver was 5°C at 620 mb (Fig. 4). Unlike the soundings, which are available only every 12 h, the RASS data (Fig. 3) shows the cooling with 1-h resolution, which helps pinpoint the timing of the frontal passage. Although the frontal features below 4 km MSL were probably strongly affected by the mountain wave and the cold surface boundary layer, there is clear evidence of cooling in the layer from 3.5 to 7.0 km MSL during the 12-h period. This cooling is maximized at 4–5 km and began sometime between 1430 and 1500 UTC. This layer of cooling rose and broadened vertically with time. Although there was little vertical shear in the layer between 4 and 5 km MSL at 1430 UTC (1.4 m s−1 km−1), possibly due to the compensating effects of baroclinicity and a downslope wind, vertical shear of 6.7 m s−1 km−1 was present in this layer by 1730 UTC and increased to 12.9 m s−1 km−1 by 2130 UTC. This lower layer was located beneath a layer that had substantially less vertical shear (e.g., 0.2 m s−1 km−1 from 6 to 8 km MSL at 1730 UTC), which itself was beneath another layer with stronger shear associated with an upper-level front near the tropopause (e.g., 11.0 m s−1 km−1 from 8 to 10 km MSL). This upper-level front was also clearly seen between 375 and 425 mb in the 0000 UTC 10 December sounding from Denver, Colorado (Fig. 4). This sounding also shows the lower frontal zone from 560 to 640 mb near a mountaintop, highlighting the fact that two vertically distinct frontal zones were located over the mountains during this event. Further evidence that the upper jet–front system in Fig. 1 is decoupled from the lower troposphere in this event is seen in wind profiler data from Medicine Bow in southeast Wyoming (not shown) where the upper-level jet moves in overhead without any preceding shear zone extending upward with time from the lower troposphere.

The cooling and increased vertical wind shear associated with the layer from 4 to 5 km MSL (Fig. 3) are characteristic of the passage of a cold front. The significant change in the character of wind profiler–observed vertical air motions (Fig. 5) in the lower and midtroposphere starting near 1330 UTC may also indicate a change in conditions related to the frontal passage. Our analysis suggests that the front crossed the instruments at mountaintop level (near 4 km MSL) sometime between 1430 and 1500 UTC on 9 December. It is also evident that a distinct upper-level front moved overhead by 1800 UTC.

b. NOAA/ERL/ETL lidar observations

A 10-μm CO2 NOAA/ERL/ETL lidar, described by Post and Cupp (1990), was operating on 9 December 1992 from Table Mountain located about 10 km north of Boulder. Data from the same lidar was used by Neiman et al. (1988) and Clark et al. (1994) to study windstorms. Observations and analyses for the present case are described in Ralph et al. (1997). Because of the unusually large amount of volcanic aerosol created by the eruption of Mt. Pinatubo in 1991 (Bernard et al. 1991), the lidar wind measurements extended well into the stratosphere (Post et al. 1996) on 9 December 1992 providing useful data for the first 2 km above ground level (AGL), and then again from near tropopause height to about 18 km AGL (Ralph et al. 1997).

Direct evidence of the mountain wave structure aloft is shown in the range–height indicator (RHI) scan at 1605 UTC (Fig. 6). Figure 6a shows unusually strong backscatter in the lower stratosphere associated with volcanic aerosols. Figure 6b shows a region of reversed (easterly) winds in the lower stratosphere near 12 km MSL and 10–15 km west of the lidar showing a breaking gravity wave, whereas east of the lidar, at the same altitude, the radial velocity is westerly at about 40 m s−1. Figures 6c and 6d show contour analyses of radial velocities as observed in the RHI (Fig. 6c) and as simulated by the model (Fig. 6d). Comparisons between Figs. 6c and 6d are discussed in section 4b. This flow structure is characteristic of large-amplitude gravity waves as shown in earlier aircraft observations (Lilly and Kennedy 1973; Lilly et al. 1982). Ralph et al. (1997) showed further evidence that this strong west-to-east gradient in radial velocity seen in Fig. 6 is also present in the vertical profiles of horizontal velocity derived from the velocity–azimuth display technique (Koscielny et al. 1982) and that a substantial horizontal gradient was maintained for several hours.

Figure 7a shows an RHI lidar scan in the SSW–NNE (210°–30°) plane that is oriented approximately normal to the northwest mean flow direction. This scan suggests the presence of a horizontal vortex near the tropopause. The red spot, in Fig. 7b, at 8.5 km AGL shows motion away from the lidar, and the green areas just above and below the red indicate motion toward the lidar. Note that these perturbations are embedded in a larger region of flow away from the lidar, which makes the areas of perturbed flow toward the lidar smaller than they would be otherwise. Figure 7c shows a contour plot of the derived radial velocities, which gives a clearer picture of the rotary motion. This figure also shows the estimated position of the tropopause. Figure 7a displays the backscatter intensity. Note that the position of the observed vortex is along the tropopause. Also note that the wavelike character of the tropopause can be identified by abrupt changes in the lidar backscatter intensity caused by discontinuities in the volcanic aerosol concentrations and the presence of clouds. The cloud is located in a position consistent with the circulation inferred by the presence of velocities directed away from the lidar (red) beneath a region of velocities toward the lidar (green). Although the region beneath the red spot also contains some pixels showing flow toward the lidar, these data are quite noisy. The red spot covers a region of about 2 km in diameter where the radial velocity is nearly 20 m s−1 away from the lidar. Using the lidar data in Fig. 7 and the model simulation for guidance, a schematic of the physical interpretation of the vortex was developed as shown in Fig. 8. Figure 8a shows the vortex aligned with the flow, whereas Fig. 8b shows a depiction looking into the flow. The cloud in Fig. 8b, as seen by the strong backscatter, is in the updraft of the HVT. Satellite cloud observations, presented in the next section, show further details regarding the structure of this cloud. Naturally our interpretation is not without some ambiguity, but it is entirely physically consistent with the motion field of an HVT.

c. DMSP satellite observations

The DMSP visible image taken within 4 min of the incident is shown in Fig. 9. The photo reveals several parallel cloud bands east of the foehn gap. Comparison with the lidar cloud observation in Fig. 7 indicates that elevations of the bands are between 10.5 and 11.5 km MSL. The black dot indicates the position of the NOAA lidar, and the plus sign the location of the aircraft incident. Using the original image it was possible to identify 12 cloud bands that were nearly parallel. Their orientation was 315° ± 6° and a spacing of 13.8 ± 3.4 km. Some bands were in excess of 200 km long. The positions of the lidar and the incident are also shown in Fig. 9 and indicate that the satellite cloud bands were present at both sites.

d. Pilot reports of clear-air turbulence

Numerous aircraft encounters with clear-air turbulence were reported near and along the eastern slope of the mountains in northern Colorado on 9 December 1992. Figure 10 shows the horizontal and vertical distribution of these reports relative to the mountains. Most notable of the turbulence encounters was that experienced by the DC-8 cargo jet at 1510 UTC, at 9.7 km MSL, at a position 50 km southwest of the lidar (Fig. 10a) (approximately 39.635°N, 105.575°W). The pilot reports (PIREPs) clearly establish that severe turbulence was present within the mountain wave and that it occurred over a wide range of altitude, but mostly downstream of the mountains (Fig. 10b). It should be noted that the temporal and spatial distribution of aircraft, as well as their type, significantly affect the number and location of turbulence reports. Variability of flight patterns, and differing aircraft responses to CAT among other factors, limit quantitative interpretation of the PIREP data (Schwartz 1996).

3. Model description

Simulations using four levels of grid refinement were performed using the Clark–Hall model (Clark 1977; Clark and Farley 1984; Clark and Hall 1991, 1996). The large-scale domain used 25.6-km horizontal grids over 820 km by 820 km and took its time-dependent boundary conditions from MAPS (Benjamin et al. 1994). The MAPS system uses all available data, including wind profilers, Aeronautical Radio, Incorporated (ARINC) Communications Addressing and Reporting System (aircraft) and others, along with a mesoscale model first guess to produce mesoscale analyses every 3 h over the continental United States. The innermost domain, using 200-m horizontal grids, focused on the turbulence over a region of 48 km on a side by 12.7 km in the vertical. The current simulations cover sufficient areal extent and range of numerical resolution to treat processes from frontal dynamics (on the large scale) to wave-induced turbulence (at the smallest scale). The topography used by the model was derived from the U.S. Defense Mapping Agency 30-s elevation data that are available from the Scientific Computing Division of the National Center for Atmospheric Research (NCAR). Figure 11 displays the topography of the outermost domain with the outline of each of the four inner domains. The outline of the state of Colorado is also shown. The resolution and relative geometries of each domain are given in Table 1.

The present experimental design is similar to that in Clark et al. (1994) but with the following generalizations. In the present study, we use large-scale initialization and time-dependent boundary conditions. A Lanczos digital time filter was used as part of the initialization (Hamming 1983). We also include the full inertial effects in both the momentum and thermodynamic equations. In the earlier study, the Coriolis terms were approximated in the momentum equations treating only perturbations from geostrophic balance. This procedure distorts large-scale inertial motions but does allow one to use cross-stream cyclic boundary conditions. This idealization was considered unacceptable for the full treatment of large-scale baroclinicity. Vertical grid stretching was also added to the model since the Clark et al. (1994) simulations.

In the present simulations the outermost vertical grid increment, Δz, varied smoothly from 50 m at the surface to 200 m at z = 425 m AGL and more gradually increased to 407 m at 4.15 km AGL. This was achieved using the stretched vertical coordinate transformation
zFζhHh,
where z and ζ are the Cartesian and transformed vertical coordinates, respectively. Here, F(ζ) is defined such that F(0) = 0 and F(H) = H, where H is the height of the outer domain. The stretching for the outer domain used the quadratic expansion
Fnnn2
for the first four grid levels, where ζn = (n − 2)Δζ and Fn = F(ζn). Matching derivatives at n = 4.5, Fn were then replaced by the the fourth-degree polynomial
Fnnn2n3n4
from levels 5 through 17 such that Δz = 407.06 m was smoothly approached. The constant value of Δz = 407.06 m was then retained throughout the troposphere and lower stratosphere. Using a hyperbolic tangent profile centered at 18 km, the grid increment was smoothly increased to Δz = 750 m for the remaining stratosphere to the model top at z = H = 27.4 km. Domains 4 and 5 used twice the vertical resolution as domains 1, 2, and 3. The vertical grid locations for the fine-scale inner domains were determined using the grid-nesting principles described by Clark and Hall (1996). This resulted in the fourth and fifth domain grids smoothly varying from 20 m near the surface to 200 m aloft free of any significant artificial oscillations. The fifth domain grid was nearly isotropic with 200-m grid spacing between 4 and 12.7 km.

The model was initialized using the 0900 UTC MAPS analysis data, and 3-hourly MAPS analysis data were used to update the model’s outermost boundaries throughout the simulation. These data were interpolated onto the model grid for initialization and the time-dependent boundary conditions. The momentum, temperature, and moisture fields were first projected onto the outermost 25.6-km grid. A potential flow adjustment was then applied to the momentum fields to ensure mass continuity was satisfied. The second domain, using a 6.4-km horizontal grid, was established using the mesh refinement procedures of Clark and Farley (1984). The two-domain system was then run for 1.5 h using a Lanczos time filter to help suppress any unphysical modes in the initialized data. A third domain was then added, using horizontal grids of 1.6 km, and the model was integrated forward until 1300 UTC. At this time a fourth domain, using a horizontal grid size of 400 m, was added with twice the vertical resolution, and the system was integrated forward 30 min before adding the fifth domain, using a horizontal grid of 200 m. The entire system was then integrated for another 3 h. The present analyses are taken between 1400 and 1500 UTC during the period when the highest-resolution domain had been established for at least 30 min.

4. Results

a. Frontal position in relation to aircraft incident

As described in section 2, a front passed over the Continental Divide between 1400 and 1800 UTC on 9 December 1992 but was not readily identified at the surface. Within the model, the front can be seen in the Hθ patterns between 4 and 7 km MSL. Figure 12 presents a time sequence of θ showing horizontal plan views of the cold air first advancing south, west of the divide, before crossing to the east of the Continental Divide. However, the evolving mountain wave and flow-aligned jet stream undulations complicate the situation. Nevertheless, the position of the leading edge of the front at 1510 UTC, the time of the aircraft incident, appears to coincide remarkably well with the position of the incident. Due to computer memory limitations and the northward positioning of the NOAA lidar data, the high-resolution grid was located just north of the incident, which was at a position corresponding to x = 28 km and y = −9 km in Fig. 12. As a result, the analysis to follow is for the leading edge of the frontal cold surge occurring approximately 1 h before and 30 km north of the aircraft incident.

b. Windstorm flow structure

A comparison between the radial velocities observed in the east–west RHI cross section and those derived from the simulated winds is shown in Figs. 6c and 6d. Comparing these figures, we see that the model accurately predicts the height of the region of flow reversal at about 12 km MSL. However, the horizontal location, at this particular time, is predicted about 7 km too far to the west. The horizontal location of the minimum u varies considerably with time in the simulations, which may account for this difference. The important thing to note is that the flow reversal region is usually well above the tropopause in both the observations and the model simulations and, as such, about 2–3 km above the CAT causing the aircraft incident.

The Cartesian components of the horizontal flow were rotated into a mean, us, and normal flow direction, un. Figures 13 and 14 show 30-min time averages of the streamwise flow, 〈us〉, and the cross-stream flow, 〈un〉, along with the vertical velocity, 〈w〉, and potential temperature, 〈θ〉, at 6.3 and 11.6 km MSL, respectively. The 6.3 km MSL was chosen because at the time shown it corresponds to a level below the jet stream maximum showing strong source regions of CAT. An episodic downburst of turbulence penetrating this level and continuing to the surface was also simulated at this time, which resulted from frontal interactions and wave breaking. A number of interesting features of this downburst of turbulence are seen at this level, such as intense linear features in the perturbation flow. We used 288° to represent the stream flow direction at the 6.3 km MSL because this corresponds to the local orientation of the jet stream. The 11.5 km MSL was chosen because it corresponds to a level in the model and observations where active internal gravity wave breaking occurred. We used 315° to represent the local stream direction at this elevation. This direction also corresponds to the orientation of cloud bands seen in the DMSP imagery.

Figure 13 shows numerous linear features aligned with the 288° mean flow direction. Both 〈un〉 and 〈w〉 show some indication of alternating sign, indicating a cross-stream wave structure. Probably the best definition of linear features is seen in Fig. 13c where 〈w〉 shows long streaks of strong downward motion. The two most prominent bands are north of y = 20 km and spaced about 13 km apart and oriented along 288°. Weaker downdrafts are also evident along the full extent of the divide giving the typical foehn gap signature to the flow. These horizontal spacings of the intense downdrafts are very close to the 14-km DMSP cloud-band spacing. The features shown in Fig. 13 are sufficiently steady with time that they can be used to define temporal standard deviations of the wind, which clearly highlight the intermittency and localization of the CAT.

Figure 14 shows the mean flow structures at 11.6 km MSL relative to 315°. Note that 〈us〉 shows well-defined regions where 〈us〉 varies between −10 and 0 m s−1. These areas represent reversals in the horizontal flow as observed by lidar (Fig. 6). Interesting features in 〈w〉 are the bands of updraft oriented in the mean flow direction corresponding very closely to the DMSP cloud-band orientation. However, the updraft spacing in Fig. 14c is about 7.8 km, or a little less than half the observed cloud spacing. Unless all the model updrafts are saturated, it is not clear that the model has underpredicted the scale of the flow-aligned undulations. The rather good comparison of orientation with the observations provides considerable credibility to the realism of the simulations. The simulated cloud water fields (not shown) were in reasonable agreement with the observations in terms of orientation and spacing but were, in general, more widespread than those observed. This frustrating level of difficulty in comparing model predictions with observed high-level cloud spacing is not surprising considering the difficulty of simulating and, particularly, initializing high-tropospheric moisture fields.

Figures 15 and 16 show the relative positioning between the jet stream and the upper-level region of internal gravity wave breaking. Figure 15 shows four vertical cross sections oriented spanwise (or normal) to the mean flow direction of 288° of the streamwise velocity, whereas Fig. 16 shows cross sections oriented spanwise to 315°. Particularly noticeable in Fig. 15 are the intense cross-stream oscillations in the jet stream aligned with the east–west-oriented upper-level frontal system. The horizontal spacing of these jet stream perturbations is about 7 km. Before concluding that our predicted scales are only about half that observed, we should consider the 〈w〉 field at 6.3 km MSL in Fig. 13 where we see considerable variation in vertical motion associated with the distorted regions of the jet stream. The regions of updraft are quite widely spaced, and the intense well-defined downdrafts are spaced about 14 km apart and extend far downstream. These results indicate a broad range of scales, but with some relevant signatures in the observed 14-km scale. Some of the darker contour shading of us in Fig. 15 shows regions where some isotachs have overturned, suggesting the presence of rather intense north–south wind shears. The 2–3-km vertical undulations of isotachs are probably associated with the long streamwise, short spanwise striations of similar scale noted in Fig. 13.

Figure 16 clearly defines regions of either weak streamwise or even-flow reversal near 11–12 km MSL. The comparison between Figs. 13 and 14 shows there is a well-defined turning back of the wind between the jet stream level and indicates where the internal gravity waves break. The turning of the wind may affect the vertical propagation of waves. For example, the simulations do not show wave amplification resulting from constructive reflections from the underside of the super-adiabatic region.

c. Horizontal vortex tubes

Figure 17 shows three three-dimensionally rendered variables of the flow at 1415 UTC with the viewer looking toward the northwest. Each figure shows an isosurface of u = 55 m s−1 in light shading depicting the jet stream. Dominant in the figures are 2-km vertical displacements in the jet stream that are spaced approximately every 8 km and were noted with respect to Fig. 15. Also in the figure are vortex structures on the southern faces of these jet stream undulations. The dark shading shows isosurfaces of the field of vorticity magnitude, |ω| (Fig. 17a); the baroclinic production of |ω| (Fig. 17b);and the |ω| production by vortex stretching (Fig. 17c). By comparing the vertical positioning of the jet stream in Fig. 15 with the three-dimensional rendering in Fig. 17, we see that the vortex structures, as shown by the depiction of |ω| in Fig. 17a, are distributed along the upper face of the jet stream between 8 and 10 km MSL. The buoyancy production (Fig. 17b) along the upper face of the jet stream accounts for the initial production of the vorticity followed by stretching as depicted in Fig. 17c. The maximum in |ω|, along with its sources, is located well below the main wave-breaking region at z ≈ 10 km MSL, which is close to the tropopause. The tubular structure of the vorticity source terms in Figs. 17b and 17c encourages us to hypothesize that increased resolution will result in flow-aligned vortices. This is based upon Kerr et al. (1996), who show that the source terms can predict the subgrid-scale vorticity. These figures show the presence of flow-aligned HVTs. They are positioned mostly on the south-facing crest of one of the jet stream undulations and occur at about the same elevation as the aircraft incident. The horizontal scale of these vortex tubes is similar to the interpretation derived from the NOAA lidar observations. The amplitude of the simulated vorticity (0.1–0.5 s) is more than strong enough to account for the incident. These values were associated with a 35 m s−1 velocity change over one vertical grid level. Estimates from the single lidar RHI give about 0.07 s−1, which seems like reasonable agreement considering the limited lidar sampling volume. The ability of an aircraft to counter the axial rolling moment of an HVT is expressed as a dimensionless maximum roll rate, which is a linear function of an aircraft-specific coefficient, airspeed, and wingspan (McCormick 1995). As this rate is a critical aspect of aircraft stability, it is specified by the Federal Aviation Regulations (FAA 1985) and a military specification (Silvers and Withers 1975). Using this specified roll rate and assuming that the DC-8 was near its published cruise speed, we calculate that for an HVT with a vorticity of 0.5, full application of controls will just match the imposed rolling moment. On the other hand, the lidar-observed 10 m s−1 vertical velocities applied to one wing or 10 m s−1 to both exceeds the maximum roll control by more than a factor of 2. The present evidence is sufficient to prompt us to hypothesize that such an HVT caused the aircraft incident of 9 December 1992.

Figure 15 shows that the tropopause has experienced oscillations of up to 2 km in amplitude. Similar oscillations were seen in the lidar data as shown in Fig. 7. The precise reason for these oscillations is not understood and is considered beyond the scope of the present paper, although some possible mechanisms are discussed in a following section. It is the horizontal variation of the tropopause surface (and jet stream) that provides the physical mechanism for the baroclinic production of the flow-aligned vorticity.

While it is obvious that an encounter with an HVT could present a challenge to aviators, this work shows that the challenge is possibly severe. An aircraft making an HVT transect approximately normal to its axis gets only a bump pitching up or down on entry and the sequence in reverse exiting. It is the oblique intersection with an HVT that presents the greatest challenge for such an event; first the intersecting wing penetrates the HVT wall, and a strong rolling moment is experienced and likely countered by appropriate application of the controls. Next the aircraft is pitched up or down as the fuselage enters the HVT and then sees a further rolling moment that is dependent on the aircraft’s current roll angle. Then crossing the HVT to its opposite wall the aircraft exits and, again, dependent on roll angle, can be rolled in either sense and pitched in the opposite sense, as on entry. While such a transect provides for considerable variation in detail, one of the worst cases is the one where the sense of the rotation is effectively the same on entry and exit, and the result could be rolled, inverted, or otherwise upset. Given the range of vortex dimensions possible, the reasonably allowed vorticities, and the mix of encounters possible, we can at this point only note that the pitching and rolling moments reported by the DC-8 crew are entirely consistent with an oblique HVT transect. As much of the apparent aviation hazard from HVTs is associated with their sheer unexpected nature, we plan on working to further refine the forcing parameters associated with various encounter scenarios. Naturally our next step in studying HVTs is to see if we have learned enough from these model and observational results that we might be able to forecast the phenomena and then observe them carefully with instrumented aircraft.

d. Turbulent downburst

Three-dimensional animations of the temporal standard deviation of the wind speed reveal a spectacular downburst of turbulent kinetic energy in the simulated windstorm. This downburst of turbulence has the visual appearance of a shaft of heavy precipitation both in shape and in the way it advects through the domain. Further analysis reveals that this event coincided with the leading edge of the cold frontal surge shown in Fig. 12. As with the HVTs, this downburst of turbulence also appears to result from interactions between the jet–front system and the downslope windstorm dynamics.

To display this event, we start by showing time sequences of w′ at 6.3 km MSL, when the turbulence is still at the level of the jet stream. Figure 18 shows a bow-shaped downdraft (hatched area) first appearing in the northwest sector of the highest-resolution domain and propagating southeast through to about the domain center in the next 7.5 min. Animations of the temporal standard deviation of the wind speed from a 30-min average, σq, indicate that the source of the perturbation kinetic energy consists of shearing instabilities over a major portion of the jet stream surface. Figure 19 shows a three-dimensional rendering of σq (light shading) overlying the jet stream (dark shading) at 1410 UTC. As in previous figures, the surface of u = 55 m s−1 is used to depict the jet stream. Isosurfaces of σq = 10 m s−1 are shown to characterize the CAT. The two arrows in Fig. 19 point to CAT source regions located on both the upper (A) and underside (B) of the jet stream. These and other source regions develop with time and all feed into a common downdraft. The underside source region is already more developed than that on the upper surface. Animations indicate that a major portion of the perturbation kinetic energy in the turbulent downburst originates from the two vertically sloping source regions on the underside of the jet. The shear layers on the top of the jet, which one would associate with conventional internal wave-breaking dynamics, account for the remaining perturbation kinetic energy feeding the downburst of CAT.

Figure 20 shows a time sequence of σq at 1 km AGL extending over a slightly later period than that shown for w′ in Fig. 18. This is designed to illustrate how the low-level turbulence, resulting from the shear flows seen in Figs. 18 and 20, propagates. A localized region of CAT first touches down about 10 km east of the divide prior to the beginning of this sequence and in the 7.5 min seen in Fig. 20 propagates from the upper center partially through to the eastern boundary of the high-resolution domain. This type of simulated surface gustiness pattern is in agreement with the reports of intermittent severe surface gusts on that day. It is also interesting to note that the largest downward vertical motions observed in the lower and middle troposphere by the wind profiler at Platteville, Colorado, were at approximately 1400 UTC, nearly the same time that the simulated turbulence downburst occurred (Fig. 5).

Excitation by the jet stream undulations appears to perturb the wave-breaking region strongly enough to force a downburst of CAT that reaches the ground and propagates southeast over the plains. Perturbation kinetic energy is fed from the top and the right and left sides of the convoluted jet stream surface and combines into a single shaft of downward penetrating CAT. After the occurrence of this penetrating downburst of CAT, the lower-level flow returns to a relatively quiescent state. This type of event is similar to the vortex tilting described in the papers by Clark et al. (1994, 1996); however, in this case the event relies on a rather complex interaction between the two nearly orthogonal wave modes, that is, the flow-aligned internal gravity waves that propagate in the mean flow direction and the jet stream undulations that propagate normal to the mean flow direction. We believe this is the first time such an event has been reported in the literature, so its importance and overall role in the arena of windstorm dynamics require further assessment.

5. Discussion of the flow-aligned jet stream undulations

Possible instabilities pertaining to this physical situation are numerous and will be discussed in this section. Before presenting possible explanations, we first review the morphology of the cross-stream jet stream undulations.

a. Jet stream undulations

Figures 15, 21, and 22 show four cross sections, aligned normal to the mean flow direction, of us, w, and un at 1415 UTC, respectively. Evident in Fig. 15 are the wavelike distortions of the jet stream that also appear in the three-dimensional perspectives of Fig. 17. As the cross sections move toward the east, the region of us > 50 m s−1 shrinks, giving better definition to the scale of the jet stream distortions. A significant increase in the horizontal gradient of us and a narrowing of the most southerly trough are evident in Figs. 15b–d. At y ≈ 30 km in Fig. 15d the northern face of the downwardly depressed jet has become extremely narrow providing the strong horizontal gradients in the dynamic and thermodynamic fields. Although seen better as downdrafts in Fig. 13c, some evidence for an approximately 14-km separation of these intense wavelike structures appears in Figs. 15c,d.

Figure 21 shows the w field for the same cross sections as in Fig. 15. There are tropospheric downdrafts throughout much of the cross-sectional domain consistent with what one might expect in the foehn gap of windstorms. This is particularly evident in Fig. 15b. However, in all four cross sections there are anomalous updrafts and downdrafts associated with the cross-stream distortions of the jet stream. Note particularly the strong downdraft at y ≈ 30 km in Figs. 15c and 15d where w < −10 m s−1. Just to the north of this downdraft is a broad region of updraft with w > 2 m s−1 associated with the upward displacement of the jet stream shown earlier. These cross-stream structures in w and u and the corresponding thermal gradients account for much of the CAT and HVTs described earlier.

Figure 22 shows the un field for the same cross sections as in Figs. 15 and 21. Note that the flow above and below the tropopause is in opposite directions in this plane of view. The most intense shear and the location of the HVTs seen in the three-dimensional visualizations of Fig. 17 are between the southward jet at roughly 10 km MSL, and the more uniform northward flow above the tropopause between y = 25 and 35. In this region the velocity field contains nonoscillatory jumps of up to 40 m s−1 between mesh points that correspond to the 0.20 s−1 vorticity mentioned earlier. The images in Fig. 22 are also the best numerical analog to the lidar images in Fig. 7. Note that by being at the tropopause, this jet and accompanying vorticity are above the strongest vertical undulations in the jet stream in Fig. 15. However, because the maximal region for the jet and the strong undulations in the jet stream below cover the same horizontal extent in y, we believe the two signatures of activity are intimately connected. A dynamical mechanism that could explain these features is discussed next.

Animations of the flow show short wavelength quasi-two-dimensional gravity waves with long linear extents parallel to the mean flow propagating downwind in their respective flow directions in this plane. The phenomena of counterpropagating gravity waves provide one possible mechanism to support the cross-flow wave structure and will be discussed in the next section.

b. Possible causal mechanisms

Instability theories of waves within stratified layers depend upon the details of the velocity and stability profiles across the tropopause inversion, which may explain some of the model solution behavior (Holmboe 1962; Caulfield 1994). Another explanation for the development of the cross-stream temperature gradients may simply be due to the flow deformation associated with breaking waves. This process is analogous to classic frontogenesis where the flow is accelerated below the wave-breaking region resulting in confluent lateral motions enhancing the cross-stream temperature gradient.

The physical mechanism leading to the cross-stream wavelike distortions in the jet stream must be consistent with the approximately 14-km scale spacings and for vertical displacements between 2 and 4 km. Possible candidates include dry symmetric instabilities (Bennetts and Hoskins 1979; Jones and Thorpe 1992) or jet stream imbalances (O’Sullivan and Dunkerton 1995) and, finally, cross-roll instabilities associated with breaking gravity waves (Klaassen and Peltier 1989; Andreassen et al. 1994; Fritts et al. 1994; Afanasyev and Peltier 1998). Strong wave excitation also appears after transient behavior of the jet stream in Fritts and Luo (1992) and van Tuyl and Young (1982). Each of these explanations has weaknesses. A more likely explanation is hydrodynamic instabilities associated with shear layers (Holmboe 1962) and is discussed next. This is followed by a discussion of the weaknesses of the other explanations. There will also be some discussion of similar horizontal spacings in recent three-dimensional simulations of windstorms by C. Schar (1997, personal communication) and J. Doyle (1997, personal communication).

Holmboe (1962) examined hydrodynamic instabilities of shear layers across an inversion for several temperature and velocity distributions. This work was an extension of the classic theory of Lord Rayleigh (1880) where he treated the same problem in the limit of no stratification. Holmboe showed that, besides the Kelvin–Helmholtz (K–H) wave, one could obtain an oscillatory instability that he referred to as an “overdamped mode,” later termed the “Holmboe instability.” It is an instability that appears when Ri > ¼. Here Ri ∼ 1 occurred across the tropopause when the waves were not overturning. One must remember that Ri > ¼ is only a necessary condition for stability. If there are inflection points in the shear profile, instabilities such as Holmboe can be important.

Holmboe showed that two trains of waves of equal wavelength moving in opposite directions symmetrically above and below an inversion layer can lead to standing wave solutions with ever-increasing amplitude. The short wavelengths propagate downstream in their respective directions, whereas the longer wavelengths interact to phase lock and amplify. Laboratory studies by Browand and Winant (1973) showed that Holmboe waves form characteristic cusps within the temperature inversion layer where the vorticity and vertical temperature inversion are locally increased. When the vorticity amplitude is large enough, material is shed from these sharp cusps. Numerical studies by Smyth et al. (1988) suggested that Holmboe waves have no inherent three-dimensional instabilities that might provide for steady high-amplitude disturbances within fields of otherwise rather chaotic disturbances.

Animations in time of the cross sections of w in Fig. 21 clearly show waves propagating just above the tropopause in the manner necessary for the Holmboe instability to occur. Below the tropopause an oscillating windstorm might be a better description of the variability, but a phase-locking mechanism does seem to be operating. Based upon these observations, laboratory comparisons are relevant. Laboratory studies by Browand and Winant (1973) showed that Holmboe waves have a similar wave structure to the spanwise waves seen in our simulations. The wavelengths expected are λ > 2πh/1.2785, where h is the depth of the shear layer. The depth of the waves running above the tropopause is less than a kilometer, which is consistent with 2–3-km amplitude oscillations. The nonlinear character of these waves shows the greatest steepening on the downstream (from the perspective of the upper flow) sides of dips, consistent with the appearance of HVTs on the south-facing slope of dips in the jet stream. Why these waves are not present across the tropopause, but appear only approximately every 14 km, probably depends on how the dynamics leading to the waves develops.

Let us now examine other possible cross-stream instability mechanisms. It is possible that one of these is responsible for the 14-km scale. However, none of these instability mechanisms provide a complete description of the features of this calculation.

The wave excitation by an unbalanced front over the mountains (Ley and Peltier 1978) is an unlikely source due to the poor definition of the front at the surface. The dry symmetric instability (Bennetts and Hoskins 1979; Jones and Thorpe 1992) predicts wave spacings that are usually considerably larger than 14 km, O(100 km) due to the long inertial timescales that drive these instabilities.

A number of researchers report the development of cross-roll instabilities in both K–H billows and breaking gravity waves forced by flow over mountainous terrain. Klaassen and Peltier (1989) presented the basic mechanism for K–H billows. Andreassen et al. (1994) and Fritts et al. (1994) showed such structures developing in high-level stratospheric internal gravity waves, and Afanasyev and Peltier (1998) showed similar features for idealized three-dimensional mountain wave flow. It is characteristic of these cross-roll instabilities to develop within the wave-breaking region, forming flow-aligned vortex pairs, which then strongly affect and modulate the local dynamics providing transient cross-roll structures. The weakness in this theory is in explaining the 14-km horizontal scale, the steadiness of the waves, and their vertical location. They are positioned well below the main wave-breaking region.

O’Sullivan and Dunkerton (1995) performed large-scale numerical simulations of the life cycle of a baroclinic disturbance, examining the creation of inertia–gravity waves due to rapid deformation of the upper-tropospheric flow. They found that this occurred primarily in the jet stream exit region of the upper troposphere and that the phase orientation of these waves was generally normal to the mean flow, which is the opposite of the dominant structures found in our simulations. Also in the simulations, the jet stream undergoes extreme imbalances close to the mountains, which would make it difficult for their mechanism to work. However, their gravity wave generation mechanism could be in line with the turbulent downburst event seen downstream of the main cross-roll instability in the simulation.

Moderately large scale cross-stream disturbance has been observed in additional model simulations. C. Schar (1997, personal communication) obtained a 20-km cross-stream structure to his idealized flows over a two-dimensional ridge, which seemed to develop downstream of their two-dimensional ridge. In this case, the lack of a three-dimensional jet stream would suggest that the localization of the jet is not the cause. Perhaps ageostrophic imbalances due to the wave-breaking region (e.g., Clark et al. 1994) help define the two layers necessary to establish a Holmboe instability. J. Doyle (1997, personal communication) obtained a similar scale structure in his simulations of flow over the shelf of Greenland and it did not appear likely that one could account for the structures through variations in the orographic forcing. It should also be noted that the resolution in a number of these cases is too low to begin to resolve cross-flow instabilities. For all these cases, cross-flow wave structures appear as a common physical response suggesting a new aspect of windstorm dynamics as researchers enter fully three-dimensional time-dependent representation of these events.

6. Conclusions

Model simulations of the 9 December 1992 Front Range windstorm were presented showing good comparisons with both the NOAA/ERL/ETL lidar and DMSP satellite observations. This was the type of windstorm where the flow above and below the jet stream maximum tended to remain detached from one another. The simulations also show that the dynamics of this windstorm was very much a result of strong interactions between two distinctly different wave forms, namely, flow-aligned internal gravity waves and cross-flow jet stream undulations. In this particular case, these two classes of wave modes were nearly orthogonal to each other. As a result, wave interactions led to windstorm dynamics providing a number of intriguing physical events such as horizontal vortex tubes (HVTs) and a penetrative downburst of CAT, which we have been able to document for the first time. Overall, the dynamics of this particular windstorm is inherently three-dimensional and hence very poorly represented by a conventional wave-breaking windstorm model.

The identification of HVTs in the simulations may well account for the aircraft incident of that day. Both the elevation and extrapolated position of the HVTs fit the event. The simulation showed them occurring between about 8 and 10 km MSL where the incident occurred at 9.7 km MSL. The amplitude of the vorticity in the simulated HVTs was sufficient to account for the type of event experienced by the DC-8 cargo plane that had 19 ft of wing plus one of its four engines sheared off. The initial source of the HVTs was identified with the baroclinicity of the highly distorted tropopause resulting from the interaction between the cross-flow jet stream undulations and the cross-mountain jet stream flow. Subsequent stretching by a streamwise burst associated with frontal passage is shown in Fig. 18. These particular HVTs did not originate in, nor propagate from, the region of breaking internal gravity waves and as such are not a result of the cross-roll instabilities found in K–H waves.

The observations and simulations showed that surface gustiness was minor with only intermittent reports of severe surface winds. The maximum gusts measured at Boulder were only 35 m s−1. The simulations identified a penetrative downdraft of CAT resulting from the interaction between the two distinct wave modes, which gave model predictions in good agreement with the observations. An arc-shaped downburst of turbulent kinetic energy appeared to result from constructive interactions between the jet stream undulations and the cross-mountain internal gravity wave flow. Perturbation kinetic energy was supplied from shear layers over the entire surface of the highly distorted jet stream. The downburst of turbulence had the appearance of a rain shaft propagating out over the plains leaving relative calm behind.

In forging links between our observations and model simulations, we have noted many similarities as well as qualitative differences between the two, but the study of HVTs provides another unexpected measure of precision. The NCAR team discovered HVTs embedded in the model domain near the aircraft incident location, whereupon the NOAA team began a search in the lidar data for the rotational HVT signature and promptly found them again in the immediate vicinity of the aircraft incident. This and the other linked similarities suggest to us that the model simulation represents more of a synthetic reality from which point-by-point reproduction of observations is not expected but a simulacrum where strong resemblances abound.

Much of the new and intriguing dynamics revealed by this case study rely upon interactions between two different wave forms. The flow-aligned or cross-mountain internal gravity waves are relatively well understood, whereas the undulations of the jet stream aligned with the upper-level front passing over the mountain are poorly understood. We could only present speculations on some of the potential mechanisms causing these jet stream undulations. It appears that waves of this nature have been a topic of research for a number of years, and their cause is still unresolved. A good understanding of the type of dynamics associated with the 9 December 1992 windstorm requires a much better knowledge of the nature of such flow-aligned undulations of the jet stream.

A number of questions remain regarding the nature of the turbulence. Quantitative analysis of the various source and sink terms for the kinetic energy and vorticity magnitude require evaluation. The detailed nature of the shear layers providing the CAT and the nature of the interaction between the two different wave forms affecting instabilities along these shear layers require further research as to the scale interactions of HVTs with aircraft.

One mechanism discussed that may account for the distorted jet stream forcing these vortices is the Holmboe instability. The phase locking between propagating gravity waves just above the tropopause and in the troposphere below may provide an explanation for the strong distortions of jet stream and subsequent interactions with the downslope wind leading to the present simulated and observed dynamics. These and other questions are topics of current research.

Acknowledgments

We thank Stan Benjamin for providing us with MAPS data and Jim Pasquotto for his assistance in preparing the manuscript and figures and with the Web page.

REFERENCES

  • Afanasyev, Y. D., and W. R. Peltier, 1998: The three-dimensionalization of stratified flow over two-dimensional topography. J. Atmos. Sci.,55, 19–39.

  • Andreassen, O., C. E. Wasberg, D. C. Fritts, and J. R. Isler, 1994: Gravity wave breaking in two and three dimensions. 1. Model description and comparison of two-dimensional evolutions. J. Geophys. Res.,99 (D), 8095–8108.

  • Armi, L., and R. Williams, 1993: The hydraulics of a stratified fluid flowing through a contraction. J. Fluid Mech.,251, 355–375.

  • Benjamin, S. G., K. J. Brundage, and L. L. Morone, 1994: The rapid update cycle. Part 1: Analysis/model description. Tech. Procedures Bull. 416, 16 pp. [Available from NOAA/NWS, Mary Howell, 13205 W/OM21 SSMC #2, 1325 East–West Highway, Silver Spring, MD 20910.].

  • Bennetts, D. A., and B. J. Hoskins, 1979: Conditional symmetric instability—A possible explanation for frontal rainbands. Quart. J. Roy. Meteor. Soc.,105, 945–962.

  • Bernard, A., D. Demaiffe, N. Mattielli, and R. S. Punongbayan, 1991:Anhydrite-bearing pumices from Mount Pinatubo: Further evidence for the existence of sulphur-rich silicic magmas. Nature,354, 139–140.

  • Brinkmann, W. A. R., 1974: Strong downslope winds at Boulder, Colorado. Mon. Wea. Rev.,102, 592–602.

  • Browand, F. K., and C. D. Winant, 1973: Laboratory observations of shear-layer instability in a stratified fluid. Bound.-Layer Meteor.,5, 67–77.

  • Caulfield, C. P., 1994: Multiple linear instability of layered stratified shear flow. J. Fluid Mech.,258, 255–285.

  • Clark, T. L., 1977: A small scale numerical model using a terrain following coordinate transformation. J. Comput. Phys.,24, 186–215.

  • ——, and W. R. Peltier, 1977: On the evolution and stability of finite-amplitude mountain waves. J. Atmos. Sci.,34, 1715–1730.

  • ——, and W. R. Farley, 1984: Severe downslope windstorm calculations in two and three spatial dimensions using anelastic interactive grid nesting: A possible mechanism for gustiness. J. Atmos. Sci.,41, 329–350.

  • ——, and W. D. Hall, 1991: Multi-domain simulations of the time dependent Navier Stokes equations: Benchmark error analyses of some nesting procedures. J. Comput. Phys.,92, 456–481.

  • ——, and ——, 1996: The design of smooth, conservative vertical grids for interactive grid nesting with stretching. J. Appl. Meteor.,35, 1040–1046.

  • ——, ——, and R. M. Banta, 1994: Two-and three-dimensional simulations of the 9 Jan 1989 severe Boulder windstorm: Comparison with observations. J. Atmos. Sci.,51, 2317–2343.

  • ——, T. Keller, J. Coen, P. Neilley, H.-M. Hsu, and W. D. Hall, 1997:Terrain-induced turbulence over Lantau Island: 7 June 1994 Tropical Storm Russ case study. J. Atmos. Sci.,54, 1795–1814.

  • Durran, D. R., 1995: Do breaking mountain waves decelerate the local mean flow? J. Atmos. Sci.,52, 4010–4032.

  • FAA, 1985: Federal aviation regulations. Part 25—Airworthiness standards, transport category airplanes. Federal Aviation Administration, 112 pp. Available from Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402.

  • Fritts, D. C., and Z. Luo, 1992: Gravity wave excitation by geostrophic adjustment of the jet stream. Part I: Two-dimensional forcing. J. Atmos. Sci.,49, 681–697.

  • ——, J. R. Isler, and O. Andreassen, 1994: Gravity wave breaking in two and three dimensions. 2. Three-dimensional evolution and instability structure. J. Geophys. Res.,99 (D), 8109–8023.

  • Hamming, R. W., 1983: Digital Filters. Prentice-Hall, 257 pp.

  • Holmboe, J., 1962: On the behavior of symmetric waves in stratified shear layers. Geofys. Publ.,24, 67–61.

  • Isler, J. R., D. C. Fritts, O. Andreassen, and C. E. Wasberg, 1994: Gravity wave breaking in two and three dimensions. 3. Vortex breakdown and transition to isotropy. J. Geophys. Res.,99 (D4), 8125–8137.

  • Jones, S., and A. J. Thorpe, 1992: The three-dimensional nature of“symmetric” instability. Quart. J. Roy. Meteor. Soc.,118, 227–258.

  • Kerr, R. M., J. A. Domaradzki, and G. Barbier, 1996: Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence. Phys. Fluids,8, 197–208.

  • Klaassen, G. P., and W. R. Peltier, 1989: The role of transverse secondary instabilities in the evolution of free shear layers. J. Fluid Mech.,202, 367–402.

  • Klemp, J. B., and D. K. Lilly, 1978: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci.,35, 78–107.

  • Koscielny, A. J., R. J. Doviak, and R. Rabin, 1982: Statistical considerations in the estimation of divergence from a single Doppler radar and application to prestorm boundary-layer observations. J. Appl. Meteor.,21, 197–210.

  • Ley, B. E., and W. R. Peltier, 1978: Wave generation and frontal collapse. J. Atmos. Sci.,35, 3–17.

  • Lilly, D. K., and E. J. Zipser, 1972: The front range windstorm of 11 January 1972: A meteorological narrative. Weatherwise,25, 56–63.

  • ——, and P. J. Kennedy, 1973: Observations of a stationary mountain wave and its associated momentum flux and energy dissipation. J. Atmos. Sci.,30, 1135–1152.

  • ——, J. M. Nicholls, R. M. Chervin, P. J. Kennedy, and J. B. Klemp, 1982: Aircraft measurements of wave momentum flux over the Colorado Rocky Mountains. Quart. J. Roy. Meteor. Soc.,108, 625–642.

  • May, P. T., K. P. Moran, and R. G. Strauch, 1989: The accuracy of RASS temperature profiles. J. Appl. Meteor.,28, 1329–1335.

  • McCormick, B. W., 1995: Aerodynamics, Aeronautics, and Flight Mechanics. 2d ed. John Wiley and Sons, 652 pp.

  • Moran, K. P., and R. G. Strauch, 1994: The accuracy of RASS temperature measurements corrected for vertical air motions. J. Atmos. Oceanic Technol.,11, 995–1001.

  • Neiman, P. J., R. M. Hardesty, M. A. Shapiro, and R. E. Cupp, 1988:Doppler lidar observations of a downslope windstorm. Mon. Wea. Rev.,116, 2265–2275.

  • ——, P. T. May, and M. A. Shapiro, 1992: Radio Acoustic Sounding System (RASS) and wind profiler observations of lower and midtropospheric weather systems. Mon. Wea. Rev.,120, 2298–2313.

  • O’Sullivan, D., and T. J. Dunkerton, 1995: Generation of inertia–gravity waves in a simulated life cycle of baroclinic instability. J. Atmos. Sci.,52, 3695–3716.

  • Peltier, W. R., and T. L. Clark, 1979: The evolution and stability of finite amplitude mountain waves—II: Mountain wave drag and severe downslope windstorms. J. Atmos. Sci.,36, 1499–1529.

  • ——, and ——, 1983: Non-linear mountain waves in two and three spatial dimensions. Quart. J. Roy. Meteor. Soc.,109, 527–548.

  • Pierrehumbert, R. T., and B. Wyman, 1985: Upstream effects of mesoscale mountains. J. Atmos. Sci.,42, 977–1003.

  • Post, M. J., and R. E. Cupp, 1990: Optimizing a pulsed Doppler lidar. Appl. Opt.,29, 4145–4158.

  • ——, A. Weickmann, K. R. Healy, R. J. Willis, and C. Grund, 1996:Comparison of Mount Pinatubo and El Chichon volcanic events:Lidar observations at 10.6 and 0.69 μm. J. Geophys. Res.,101, 3929–3940.

  • Ralph, F. M., M. Crochet, and S. V. Venkateswaran, 1992: A study of mountain lee waves using clear-air radar. Quart. J. Roy. Meteor. Soc.,118, 597–627.

  • ——, P. J. Neiman, and D. Levinson, 1997: Lidar observations of a breaking mountain wave associated with extreme turbulence. Geophys. Res. Lett.,24, 663–666.

  • Rayleigh, Lord, 1880: On the stability and instability of certain fluid motions. Proc. London. Math. Soc.,11, 57–75.

  • Richard, E., P. Mascart, and E. C. Nickerson, 1989: The role of surface friction in downslope windstorms. J. Appl. Meteor.,28, 241–251.

  • Rottman, J. W., and R. B. Smith, 1989: A laboratory model of severe downslope winds. Tellus,41A, 401–415.

  • Schwartz, B., 1996: The quantitative use of PIREPS in developing aviation weather guidance products. Wea. Forecasting,11, 372–384.

  • Silvers, C. L., and C. C. Withers, 1975: Evaluation of the flying qualities requirements of MIL-F-8785B. Air Force Flight Dynamics Lab Rep. AFFDL-TR-75-3, 333 pp. NTIS AD-A011 728/3/XAB.

  • Smith, R. B., 1976: The generation of lee waves by the Blue Ridge. J. Atmos Sci.,33, 507–519.

  • ——, 1987: Aerial observations of the Yugoslavian Bora. J. Atmos. Sci.,44, 269–297.

  • Smyth, W. D., G. P. Klaassen, and W. R. Peltier, 1988: Finite amplitude Holmboe waves. Geophys. Astrophys. Fluid Dyn.,43, 181–222.

  • van Tuyl, A. H., and J. A. Young, 1982: Numerical simulation of nonlinear jet streak adjustment. Mon. Wea. Rev.,110, 2038–2054.

Fig. 1.
Fig. 1.

A 300-mb analysis of geopotential height (bold solid) and wind speed (m s−1, thin solid; shading: 40–50 and 60–70 m s−1) at (a) 1200 UTC 9 Dec 1992 and (b) 0000 UTC 10 Dec 1992. The 300-mb wind vector flags are 25 m s−1, full barbs are 10 m s−1, and half-barbs are 2.5 m s−1. Wind vectors with solid-dot heads are wind profiler observations, without heads are rawinsonde observations, and stand-alone solid dots are rawinsonde thermodynamic observations.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 2.
Fig. 2.

Time–height section of hourly averaged wind profiles and total wind speed (m s−1, thin solid) observed by the 404-MHz wind profiler at Platteville, CO, between 0530 and 2230 UTC 9 Dec 1992. (a) Every other range gate is shown. Wind flags and barbs, and isotach shading are as in Fig. 1. The dashed lines represent the intermediate 35 m s−1 isotach. (b) A simulated profile from domain 3 between 1000 and 1700 UTC. The heavy dashed lines in (a) denote the boundaries of (b).

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 3.
Fig. 3.

Hourly averaged profiler wind (m s−1) and RASS potential temperature (K) θυ data between 2330 UTC 8 Dec and 2330 UTC 9 Dec 1992. Wind speed shown in bold gray shade and westerly component as dashed. Winds taken from the 404-MHz Platteville profiler. Here, θυ is shown as thin solid with regions of poor RASS coverage shown as dashed. Data taken from the 50-MHz Platteville above 3 km MSL and from the 915-MHz Erie, CO, profiler/RASS systems below 3 km MSL. Hourly averaged surface winds measured at Boulder are included. Wind flags and barbs are as in Fig. 1.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 4.
Fig. 4.

Skew-T, logp plot of temperature and dewpoint temperature (°C) from the Denver, CO, rawinsonde ascents. The companion wind profiles are also shown. Wind flags and barbs are as in Fig. 1.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 5.
Fig. 5.

Vertically stacked w time series from the 404-MHz wind profiler at Platteville, CO, between 0600 and 2300 UTC 9 Dec 1992 (scale lower right). The data were smoothed using a single pass of a temporal Hann filter. Every other range gate is shown. Approximately six data points were deemed “bad” and subjectively edited. Those bad points (approximately one-half), which were surrounded by good data, were given new values determined by linear temporal interpolation. The shaded area between 10 and 11 km marks the approximate position of the tropopause. The bold dot marks the aircraft incident.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 6.
 Fig. 6.

(a) Backscattered power measured by the Doppler lidar in a west–east RHI at 1605 UTC 9 Dec 1992. Radial velocity (Vr, m s−1) is shown in (b) as color-contoured raw data, (c) as line-contoured data. (d) An RHI of radial velocities derived from the simulated winds at the same time and positions as in (c). Negative (positive) values are toward (away from) the lidar. The scan took 60 s using a scan rate of 3° s−1. Three-

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 6.
Fig. 6.

(Continued) pulse averaging was used to calculate Vr at 3 Hz. The pulse volume is 300 m long and 0.9 m wide at 10 km range and is shown for reference. Lenticular clouds and the tropopause are also shown in (c) based on the distribution of backscattered power in (a). The tropopause in (d) is derived using θ data. The smoothed mountain profile is shown in gray. From Ralph et al. (1997).

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 7.
Fig. 7.

(a) Backscattered power measured by the Doppler lidar in SSW–NNE (210°–30°) RHI scan at 1552 UTC 9 Dec 1992. Radial velocity (Vr, m s−1) is shown in (b) as color-contoured raw data and (c) as line-contoured data. Negative (positive) values are toward (away from) the lidar. The tropopause, based on backscatter power measurements, is marked by the solid line.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 8.
Fig. 8.

(a) Schematic showing a geometric interpretation of the HVT and (b) disturbed tropopause surface in Fig. 7.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 9.
Fig. 9.

Defense Meteorological Satellite image taken of eastern Colorado at 1506 UTC Dec 1992. The white + indicates the location of the aircraft incident and the black • indicates the lidar position.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 10.
Fig. 10.

Base map and pilot reports for 9 Dec 1992. (a) Base map of northeastern Colorado showing terrain contours (500-m intervals;darkest shading is >3500 m MSL), instrument locations (P, E, and S, represent Platteville, Erie, and Stapleton wind profiler/RASS locations), pilot reports of turbulence (see legend for intensity), and the location of an aircraft accident at 1510 UTC.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 10.
Fig. 10.

(Continued) (b) Cross-mountain cross section showing the positions of pilot turbulence reports (see legend for intensity) between 39.5° and 40.3°N. Labeled times are to the nearest hour (UTC). Dots mark the precise locations of the turbulence reports, when available, and “several” refers to several reports in that vicinity. The positions of the lidar-observed tropopause and flow reversal at 1600 UTC are shown, as are the positions of the aircraft accident at 1510 UTC, the Doppler lidar, and the Platteville wind profiler.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 11.
Fig. 11.

Topography of the outermost domain with the outline of the four inner domains. The thin outline shows the state boundaries of Colorado. Contour interval is 250 m. BOU, DEN, GJT, and CSP refer to Boulder, Denver, Grand Junction, and Colorado Springs, respectively.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 12.
Fig. 12.

Time sequence of the 10-min average 〈θ〉 at 4659 m MSL from the fourth domain (400 m × 400 m grids). The thick solid lines show the underlying topography (250-m interval). Temperatures shown range between 288.52 and 293.91 K. The locations of the lidar and the aircraft incident are marked with Xs.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 13.
Fig. 13.

Temporally averaged fields from the fifth domain at 6287 m MSL at 1410 UTC. Averaging period is 30 min. Shown are (a) streamwise flow 〈us〉, (b) cross-stream flow 〈un〉, (c) vertical velocity 〈w〉, and (d) potential temperature 〈θ〉. The streamwise direction was defined as WNW 288°. The solid lines show the underlying topography (250-m interval). Vectors show nonaveraged horizontal winds.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 14.
Fig. 14.

Same as Fig. 13 except at 11 583 m MSL. The streamwise direction was defined as WNW 315°. Vectors show nonaveraged horizontal winds.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 15.
Fig. 15.

Streamwise velocity 〈us〉 at 1415 UTC on four vertical cross-stream planes oriented normal to 288°. Horizontal scale shown is for y axis, whereas actual distances are 1.05 times larger. Isentropes are shown as broken contours and velocities are shown using a grayscale.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 16.
Fig. 16.

Streamwise velocity 〈us〉 at 1415 UTC on four vertical cross-stream planes oriented normal to 315°. Horizontal scale shown is for y axis, whereas actual distances are 1.41 times larger. Isentropes are shown as broken contours.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 17.
 Fig. 17.

Three-dimensional perspectives of the simulated flow at 1415 UTC with the viewer looking toward the northwest. Each figure shows the isosurface of u = 55 m s−1 in light gray. The black isosurfaces show (a) |ω| = 0.20 s−1; (b) the buoyancy production term for |ω|, (gωxByωyBx)1/3 = 0.026s−1, where Bx and By are the x and y derivatives of buoyancy; and (c) the stretching production term for |ω|, (ωieijωj)1/3 = 0.03 s−1, where ω = × u and eij = (∂ui/∂xj + ∂uj/∂xi)/2.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 18.
Fig. 18.

Time sequence of the perturbation vertical velocity, w′, at 6287 m MSL from the fifth domain.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 19.
Fig. 19.

Three-dimensional rendering of jet stream and σq. The red shows the surface of u = 55 m s−1 and the yellow shows the surface of σq = 10 m s−1. Arrows point to sources of CAT discussed in text.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 20.
Fig. 20.

Time sequence of σq at 1066 m AGL. Thick dark contours show orography in increments of 250 m.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 21.
Fig. 21.

Total vertical velocity, w, on four vertical cross-stream planes at 1415 UTC. Horizontal scale shown is for y axis, whereas actual distances are 1.05 times larger.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Fig. 22.
Fig. 22.

Cross-stream or spanwise velocity un on four cross-stream planes at 1415 UTC. The streamwise direction was defined as WNW 288°. Horizontal scale shown is for y axis, whereas actual distances are 1.05 times larger.

Citation: Journal of the Atmospheric Sciences 57, 8; 10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2

Table 1.

Description of nested grid domain. Here, Δx, Δy, and Δz are the grid resolutions; NX, NY, and NZ are the number of points used in the x, y, and z directions, respectively; Δtmin is the minimum time step; and X0 and Y0 are the coordinates of the southwest corner of any domain relative to domain number 1.

Table 1.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation.

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