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  • Author or Editor: D. K. LILLY x
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D. K. Lilly

Abstract

An analysis is made of Gage's proposal that the horizontal energy spectrum at mesoscale wavelengths is produced by upscale energy transfer through quasi-two-dimensional turbulence. It is suggested that principal sources of such energy can be found in decaying convective clouds and thunderstorm anvil outflows. These are believed to evolve similarly to the wake of a moving body in a stably stratified flow. Following the scale analysis by Riley, Metcalfe and Weissman it is expected that, in the presence of strong stratification, initially three-dimensionally isotropic turbulence divides roughly equally into gravity waves and stratified (quasi-two- dimensional) turbulence. The former then propagates away from the generation region, while the latter propagates in spectral space to larger scales, forming the −5/3 upscale transfer spectrum predicted by Kraichnan. Part of the energy of the stratified turbulence is recycled into three-dimensional turbulence by shearing instability, but the upscale escape of only a few percent of the total energy released by small-scale turbulence is apparently sufficient to explain the observed mesoscale energy spectrum of the troposphere. A close analogy is found between the turbulence-gravity wave exchanges considered here and the turbulence-β-wave exchanges discussed by Rhines and Williams.

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D. K. Lilly

Abstract

A detailed analysis is presented of the large-scale, mesoscale and turbulent-scale features of a major downslope windstorm event in central Colorado on 11 January 1972. The storm is found to be associated with a moderate amplitude baroclinic disturbance moving across the northwestern United States within an intense zonal current. Optimal conditions for strong mountain wave generation are detectable from sounding data 12–24 h in advance and about 1000 km upstream. The mesoscale structure is dominated by a single quasi-hydrostatic wave of extreme amplitude and variable location, with corresponding variations in the windstorm structure.

Severe to extreme aircraft turbulence is observed in a deep boundary layer over the region of strong surface winds and also in a separate mid-tropospheric turbulence zone. Analysis of the latter shows that it originates in a region of intense wave-generated shear and is then carried downstream by the mean flow and upward by the wave motion. Energy generation and dissipation rates of order 1 m2 s−3 are observed. Comparisons of the turbulence features with the theoretical solutions for shearing instability by Tanaka and by Lee and Merkine show fair agreement.

Effects of the wave-windstorm-turbulence event on the larger scales are complex, involving both a substantial removal of westerly momentum and a three-dimensional redistribution of mass.

Hazards to aircraft from this kind of event are illustrated and discussed. Avoidance by vertical path deviation in found to be impractical.

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D. K. Lilly
and
Peter F. Lester

Abstract

Detailed stratospheric wind and temperature data were gathered by aircraft over the mountains of southern Colorado on 1 March 1970. In a unique operation, two instrumented RB-57F aircraft flew a total of twelve upwind and downwind legs at altitudes of 13 to 20km,.with an average separation of 600 m.

The observational data show that the stratosphere was disturbed by sporadically-turbulent gravity waves of length 20–30 km, which were apparently generated directly or indirectly by the mountainous terrain. Wave amplitudes and turbulence frequency showed a general increase with height up to about 17 km, where they reached a maximum. The maximum amplitude layer was also characterized by a minimum in the mean wind speed.

The horizontal and vertical velocity and temperature variances and covariances were evaluated and found to be generally consistent with predictions of linear gravity wave theory. The spectra of horizontal kinetic and potential energy were also calculated and appear to follow a −3 law over about a decade in wavenumber space. The covariance of the horizontal and vertical velocity perturbations is everywhere negative, with a mean downward momentum flux of about ∼2 dyn cm−2. The correlation spectra show that most of this momentum flux is contributed by the long waves.

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D. K. Lilly
and
P. J. Kennedy

Abstract

Analysis is presented of data obtained from instrumented aircraft flying in a mountain wave of moderate amplitude west of Denver, Colo., on 17 February 1970. Emphasis is placed on determination of the downward flux of westerly momentum generated by the wave, for which accurate measurements of vertical velocities on scales of order 50 km are essential. Three different methods are applied and compared: direct aircraft measurement, using vanes and an inertial platform; evaluation from the steady-state equation for conservation of potential temperature; and integration of the steady-state continuity equation. Each method produces errors, but by combining the results of the three methods a profile is obtained which agrees. fairly well with a steady-state theoretical prediction. An important side result is the discovery that gust-probe equipment is apparently not necessary for the direct aircraft measurement of wave momentum flux, but an inertial platform or similarly stable attitude reference level is essential.

A region of severe turbulence at 100 mb is found to he associated with the source of most of the downward wave momentum flux. Measurements of the loss of total energy along isentropes are found to he consistent with kinetic energy losses estimated from momentum flux divergence and with energy dissipation estimated from inertial-range aircraft measurements of the turbulent energy spectrum.

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J. B. Klemp
and
D. K. Lilly

Abstract

A numerical model is developed for simulating the flow of stably stratified nonrotating air over finite-amplitude, two-dimensional mountain ranges. Special attention is paid to accurate treatment of internal dissipation and to formulation of an upper boundary region and lateral boundary conditions which allow upward and lateral propagation of wave energy out of the model. The model is hydrostatic and uses potential temperature for the vertical coordinate. A local adjustment procedure is derived to parameterize low Richardson number instability. The model behavior is tested against analytic theory and then applied to a variety of idealized and real flow situations, leading to some new insights and new questions on the nature of large-amplitude mountain waves. The model proves to be effective in simulating the structure of two observed cases of strong mountain waves with very different characteristics.

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Y. L. Kogan
,
M. P. Khairoutdinov
,
D. K. Lilly
,
Z. N. Kogan
, and
Qingfu Liu

Abstract

A new large eddy simulation (LES) stratocumulus cloud model with an explicit formulation of micro-physical processes has been developed, and the results from three large eddy simulations are presented to illustrate the effects of the stratocumulus-topped boundary layer (STBL) dynamics on cloud microphysical parameters. The simulations represent cases of a well-mixed and a radiatively driven STBL. Two of the simulations differ only in the ambient aerosol concentration and show its effect on cloud microphysics. The third simulation is based on the data obtained by Nicholls, and the simulation results from this case are contrasted with his measurements. Cloud-layer dynamical parameters and cloud droplet spectra are in reasonably good agreement with observations.

As demonstrated by the results of three large eddy simulations presented in the paper, the cloud microphysical parameters are significantly affected by cloud dynamics. This is evidenced by the sensitivity of the cloud drop spectra itself, as well as by that of the integral parameters of the spectra, such as mean radii and droplet concentration. Experiments presented here also show that cloud microstructure is significantly asymmetric between updrafts and downdrafts. Mixing with dry air from the inversion may significantly enhance evaporation and result in cloud-free zones within the cloud. As a result of mixing, the cloud layer is very inhomogeneous, especially near its top and bottom.

The authors analyze in detail the fine structure of the supersaturation field and suggest an explanation for the formation of the model-predicted supersaturation peak near the cloud top. The LES results suggest that super-saturation may have a sharp increase in near-saturated parcels that undergo forced vertical displacement at the cloud-layer top. The main forcing mechanism that may supply the additional energy for the forced convection in the case presented is from propagating gravity waves. Although radiative cooling may also result in increased convective activity at cloud top, the sensitivity tests presented here suggest that, at least in these simulations, this effect is not dominant.

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