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- Author or Editor: D. L. Keller x
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Abstract
In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property or orthogonality has been preserved. Flow equations in general curvilinear coordinate maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible modern using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.
Abstract
In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property or orthogonality has been preserved. Flow equations in general curvilinear coordinate maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible modern using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.
Abstract
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Abstract
An analytical model is presented that accommodates nonhydrostatic shearing stratified flow over an obstacle, and that can be modified to include a superposed stratosphere with constant wind and higher stability. A simulation code is used in parallel with the analytic calculations to demonstrate a methodology for determining the wavelength and magnitude of gravity wave energy reflected, and that transmitted, by the tropopause.
Abstract
An analytical model is presented that accommodates nonhydrostatic shearing stratified flow over an obstacle, and that can be modified to include a superposed stratosphere with constant wind and higher stability. A simulation code is used in parallel with the analytic calculations to demonstrate a methodology for determining the wavelength and magnitude of gravity wave energy reflected, and that transmitted, by the tropopause.
Abstract
Previous studies have observed upstream-propagating modes in two-dimensional numerical simulations of idealized flow over topography with moist, nearly neutral conditions in the troposphere, topped by a stable stratosphere. The generation and propagation mechanisms for these modes were attributed to localized and dramatic changes in stability induced by the desaturation of the flow impinging on the mountain. In the present paper it is shown that these modes are transient upstream-propagating gravity waves, which are a fundamental feature of both moist and dry flow over topography of a two-layer troposphere–stratosphere atmospheric profile impulsively started from rest. The mode selection and propagation speeds of these transient waves are highly dependent on the tropospheric stability, as well as the wind speed and tropopause depth. In the moist case these modes appear to propagate according to an effective static stability that is intermediate to the normal dry stability and the lower moist stability. Comparisons with the linear, time-dependent, hydrostatic analytic solution show that these modes are similar to the transients observed in flow of a constant wind and stability layer over topography with a rigid upper boundary.
Abstract
Previous studies have observed upstream-propagating modes in two-dimensional numerical simulations of idealized flow over topography with moist, nearly neutral conditions in the troposphere, topped by a stable stratosphere. The generation and propagation mechanisms for these modes were attributed to localized and dramatic changes in stability induced by the desaturation of the flow impinging on the mountain. In the present paper it is shown that these modes are transient upstream-propagating gravity waves, which are a fundamental feature of both moist and dry flow over topography of a two-layer troposphere–stratosphere atmospheric profile impulsively started from rest. The mode selection and propagation speeds of these transient waves are highly dependent on the tropospheric stability, as well as the wind speed and tropopause depth. In the moist case these modes appear to propagate according to an effective static stability that is intermediate to the normal dry stability and the lower moist stability. Comparisons with the linear, time-dependent, hydrostatic analytic solution show that these modes are similar to the transients observed in flow of a constant wind and stability layer over topography with a rigid upper boundary.
Abstract
The forecast skill of upper-level turbulence diagnostics is evaluated using available turbulence observations [viz., pilot reports (PIREPs)] over East Asia. The six years (2003–08) of PIREPs used in this study include null, light, and moderate-or-greater intensity categories. The turbulence diagnostics used are a subset of indices in the Graphical Turbulence Guidance (GTG) system. To investigate the optimal performance of the component GTG diagnostics and GTG combinations over East Asia, various statistical evaluations and sensitivity tests are performed. To examine the dependency of the GTG system on the operational numerical weather prediction (NWP) model, the GTG system is applied to both the Regional Data Assimilation and Prediction System (RDAPS) analysis data and Global Forecasting System (GFS) analysis and forecast data with 30-km and 0.3125° (T382) horizontal grid spacings. The dependency of the temporal variation in the PIREP and GFS data and the forecast lead time of the GFS-based GTG combination are also investigated. It is found that the forecasting performance of the GTG system varies with year and season according to the annual and seasonal variations in the large-scale atmospheric conditions over the East Asia region. The wintertime GTG skill is the highest, because most GTG component diagnostics are related to jet streams and upper-level fronts. The GTG skill improves as the number of PIREP samples and the vertical resolution of the underlying NWP analysis data increase, and the GTG performance decreases as the forecast lead time increases from 0 to 12 h.
Abstract
The forecast skill of upper-level turbulence diagnostics is evaluated using available turbulence observations [viz., pilot reports (PIREPs)] over East Asia. The six years (2003–08) of PIREPs used in this study include null, light, and moderate-or-greater intensity categories. The turbulence diagnostics used are a subset of indices in the Graphical Turbulence Guidance (GTG) system. To investigate the optimal performance of the component GTG diagnostics and GTG combinations over East Asia, various statistical evaluations and sensitivity tests are performed. To examine the dependency of the GTG system on the operational numerical weather prediction (NWP) model, the GTG system is applied to both the Regional Data Assimilation and Prediction System (RDAPS) analysis data and Global Forecasting System (GFS) analysis and forecast data with 30-km and 0.3125° (T382) horizontal grid spacings. The dependency of the temporal variation in the PIREP and GFS data and the forecast lead time of the GFS-based GTG combination are also investigated. It is found that the forecasting performance of the GTG system varies with year and season according to the annual and seasonal variations in the large-scale atmospheric conditions over the East Asia region. The wintertime GTG skill is the highest, because most GTG component diagnostics are related to jet streams and upper-level fronts. The GTG skill improves as the number of PIREP samples and the vertical resolution of the underlying NWP analysis data increase, and the GTG performance decreases as the forecast lead time increases from 0 to 12 h.
Abstract
Numerical simulations of terrain-induced turbulence associated with airflow over Lantau Island of Hong Kong are presented. Lantau is a relatively small island with three narrow peaks rising to between 700 and 950 m above mean sea level. This research was undertaken as part of a project to better understand and predict the nature of turbulence and shear at the new airport site on the island of Chek Lap Kok, which is located to the lee of Lantau. Intensive ground and aerial observations were taken from May through June 1994, during the Lantau Experiment (LANTEX). This paper focuses on flow associated with the passage of Tropical Storm Russ on 7 June 1994, during which severe turbulence was observed.
The nature of the environmental and topographic forcing on 7 June 1994 resulted in the turbulence and shear being dominated by the combination of topographic effects and surface friction. High-resolution numerical simulations, initialized using local sounding data, were performed using the Clark model. The simulation results indicate that gravity-wave dynamics played a very minor role in the flow distortion and generation of turbulence. As a result of this flow regime, relatively high vertical and horizontal resolution was required to simulate the mechanically generated turbulence associated with Tropical Storm Russ.
Results are presented using a vertical resolution of 10 m near the surface and with horizontal resolutions of both 125 and 62.5 m over local, nested domains of about 13–24 km on a side. The 125-m model resolution simulated highly distorted flow in the lee of Lantau, with streaks emanating downstream from regions of sharp orographic gradients. At this resolution the streaks were nearly steady in time. At the higher horizontal resolution of 62.5 m the streaks became unstable, resulting in eddies advecting downstream within a distorted streaky mean flow similar to the 125-m resolution simulation. The temporally averaged fields changed little with the increase in resolution; however, there was a three- to fourfold increase in the temporal variability of the flow, as indicated by the standard deviation of the wind from a 10-min temporal average. Overall, the higher resolution simulations compared quite well with the observations, whereas the lower resolution cases did not. The high-resolution experiments also showed a much broader horizontal and vertical extent for the transient eddies. The depth of orographic influence increased from about 200 m to over 600 m with the increase in resolution. A physical explanation, using simple linear arguments based on the blocking effects of the eddies, is presented. The nature of the flow separation is analyzed using Bernoulli’s energy form to display the geometry of the separation bubbles. The height of the 80 m2 s−2 energy surface shows eddies forming in regions of large orographic gradients and advecting downstream.
Tests using both buoyancy excitation and stochastic backscatter to parameterize the underresolved dynamics at the 125-m resolution are presented, as well as one experiment testing the influence of static stability suppressing turbulence development. All these tests showed no significant effect. Implications of these results to the parameterization of mechanically induced turbulence in complex terrain are discussed.
Abstract
Numerical simulations of terrain-induced turbulence associated with airflow over Lantau Island of Hong Kong are presented. Lantau is a relatively small island with three narrow peaks rising to between 700 and 950 m above mean sea level. This research was undertaken as part of a project to better understand and predict the nature of turbulence and shear at the new airport site on the island of Chek Lap Kok, which is located to the lee of Lantau. Intensive ground and aerial observations were taken from May through June 1994, during the Lantau Experiment (LANTEX). This paper focuses on flow associated with the passage of Tropical Storm Russ on 7 June 1994, during which severe turbulence was observed.
The nature of the environmental and topographic forcing on 7 June 1994 resulted in the turbulence and shear being dominated by the combination of topographic effects and surface friction. High-resolution numerical simulations, initialized using local sounding data, were performed using the Clark model. The simulation results indicate that gravity-wave dynamics played a very minor role in the flow distortion and generation of turbulence. As a result of this flow regime, relatively high vertical and horizontal resolution was required to simulate the mechanically generated turbulence associated with Tropical Storm Russ.
Results are presented using a vertical resolution of 10 m near the surface and with horizontal resolutions of both 125 and 62.5 m over local, nested domains of about 13–24 km on a side. The 125-m model resolution simulated highly distorted flow in the lee of Lantau, with streaks emanating downstream from regions of sharp orographic gradients. At this resolution the streaks were nearly steady in time. At the higher horizontal resolution of 62.5 m the streaks became unstable, resulting in eddies advecting downstream within a distorted streaky mean flow similar to the 125-m resolution simulation. The temporally averaged fields changed little with the increase in resolution; however, there was a three- to fourfold increase in the temporal variability of the flow, as indicated by the standard deviation of the wind from a 10-min temporal average. Overall, the higher resolution simulations compared quite well with the observations, whereas the lower resolution cases did not. The high-resolution experiments also showed a much broader horizontal and vertical extent for the transient eddies. The depth of orographic influence increased from about 200 m to over 600 m with the increase in resolution. A physical explanation, using simple linear arguments based on the blocking effects of the eddies, is presented. The nature of the flow separation is analyzed using Bernoulli’s energy form to display the geometry of the separation bubbles. The height of the 80 m2 s−2 energy surface shows eddies forming in regions of large orographic gradients and advecting downstream.
Tests using both buoyancy excitation and stochastic backscatter to parameterize the underresolved dynamics at the 125-m resolution are presented, as well as one experiment testing the influence of static stability suppressing turbulence development. All these tests showed no significant effect. Implications of these results to the parameterization of mechanically induced turbulence in complex terrain are discussed.
Abstract
Mountain-wave turbulence in the presence of directional wind shear over the Rocky Mountains in Colorado is investigated. Pilot reports (PIREPs) are used to select cases in which moderate or severe turbulence encounters were reported in combination with significant directional wind shear in the upstream sounding from Grand Junction, Colorado (GJT). For a selected case, semi-idealized numerical simulations are carried out using the WRF-ARW atmospheric model, initialized with the GJT atmospheric sounding and a realistic but truncated orography profile. To isolate the role of directional wind shear in causing wave breaking, sensitivity tests are performed to exclude the variation of the atmospheric stability with height, the speed shear, and the mountain amplitude as dominant wave breaking mechanisms. Significant downwind transport of instabilities is detected in horizontal flow cross sections, resulting in mountain-wave-induced turbulence occurring at large horizontal distances from the first wave breaking point (and from the orography that generates the waves). The existence of an asymptotic wake, as predicted by Shutts for directional shear flows, is hypothesized to be responsible for this downwind transport. Critical levels induced by directional wind shear are further studied by taking 2D power spectra of the magnitude of the horizontal velocity perturbation field. In these spectra, a rotation of the most energetic wave modes with the background wind, as well as perpendicularity between the background wind vector and the wavenumber vector of those modes at critical levels, can be found, which is consistent with the mechanism expected to lead to wave breaking in directional shear flows.
Abstract
Mountain-wave turbulence in the presence of directional wind shear over the Rocky Mountains in Colorado is investigated. Pilot reports (PIREPs) are used to select cases in which moderate or severe turbulence encounters were reported in combination with significant directional wind shear in the upstream sounding from Grand Junction, Colorado (GJT). For a selected case, semi-idealized numerical simulations are carried out using the WRF-ARW atmospheric model, initialized with the GJT atmospheric sounding and a realistic but truncated orography profile. To isolate the role of directional wind shear in causing wave breaking, sensitivity tests are performed to exclude the variation of the atmospheric stability with height, the speed shear, and the mountain amplitude as dominant wave breaking mechanisms. Significant downwind transport of instabilities is detected in horizontal flow cross sections, resulting in mountain-wave-induced turbulence occurring at large horizontal distances from the first wave breaking point (and from the orography that generates the waves). The existence of an asymptotic wake, as predicted by Shutts for directional shear flows, is hypothesized to be responsible for this downwind transport. Critical levels induced by directional wind shear are further studied by taking 2D power spectra of the magnitude of the horizontal velocity perturbation field. In these spectra, a rotation of the most energetic wave modes with the background wind, as well as perpendicularity between the background wind vector and the wavenumber vector of those modes at critical levels, can be found, which is consistent with the mechanism expected to lead to wave breaking in directional shear flows.
Abstract
Two cases of observed widespread moderate-or-greater (MOG) clear-air turbulence (CAT) in different synoptic patterns are investigated using a nested high-resolution NWP model. Both of these cases occurred in confluent entrance regions of upper-tropospheric–lower-stratospheric (UTLS) jet streaks, where large-scale anticyclonic outflow from distant organized moist convection strengthened the UTLS jet. Both the strength and vertical sharpness of the resulting jet influence the altitudes of MOG turbulence and the details of simulated turbulence onset mechanisms. In a strong and narrow UTLS jet downstream of a weak synoptic ridge, MOG turbulence arises from Kelvin–Helmholtz (KH) waves that overturn in opposite directions on the vertical flanks of the jet. In broader UTLS jets, MOG turbulence arising from KH waves was favored in strong vertical shear layers beneath the wind maximum, but was inhibited above it due to static stability increases near the tropopause. However, vertically propagating internal gravity waves initiated above KH wave breaking beneath the UTLS jet amplify within the lower stratosphere above the jet, constituting another possible source of turbulence. Turbulence onset mechanisms were often apparent in simulations with minimum horizontal grid spacings of Δx = 1 km. However, amplitudes of the associated grid-resolved vertical motions were unreliable when compared with simulations having minimum horizontal grid spacings of Δx = 1/3 km. In spite of this, turbulence forecasting systems driven by input from coarser-resolution operational NWP models are demonstrated to provide good diagnoses of this type of convectively influenced CAT when the NWP model accurately forecasts upstream convection.
Significance Statement
In this study we document the role of distant convection on observed widespread strong clear-air turbulence near upper-level jet streams in different weather patterns. Results from nested NWP model simulations, together with similar examples from previous case studies, suggest a strong association of widespread turbulence with jet stream enhancements related to outflow from upstream convection. We also demonstrate how model horizontal grid spacings of <1 km are required to adequately resolve common turbulence onset mechanisms (e.g., Kelvin–Helmholtz instability, gravity wave breaking). Nevertheless, examples are provided showing that turbulence forecasting systems driven by lower-resolution operational NWP models can provide potentially valuable guidance on these widespread turbulence events when those models accurately forecast the timing and locations of upstream convection.
Abstract
Two cases of observed widespread moderate-or-greater (MOG) clear-air turbulence (CAT) in different synoptic patterns are investigated using a nested high-resolution NWP model. Both of these cases occurred in confluent entrance regions of upper-tropospheric–lower-stratospheric (UTLS) jet streaks, where large-scale anticyclonic outflow from distant organized moist convection strengthened the UTLS jet. Both the strength and vertical sharpness of the resulting jet influence the altitudes of MOG turbulence and the details of simulated turbulence onset mechanisms. In a strong and narrow UTLS jet downstream of a weak synoptic ridge, MOG turbulence arises from Kelvin–Helmholtz (KH) waves that overturn in opposite directions on the vertical flanks of the jet. In broader UTLS jets, MOG turbulence arising from KH waves was favored in strong vertical shear layers beneath the wind maximum, but was inhibited above it due to static stability increases near the tropopause. However, vertically propagating internal gravity waves initiated above KH wave breaking beneath the UTLS jet amplify within the lower stratosphere above the jet, constituting another possible source of turbulence. Turbulence onset mechanisms were often apparent in simulations with minimum horizontal grid spacings of Δx = 1 km. However, amplitudes of the associated grid-resolved vertical motions were unreliable when compared with simulations having minimum horizontal grid spacings of Δx = 1/3 km. In spite of this, turbulence forecasting systems driven by input from coarser-resolution operational NWP models are demonstrated to provide good diagnoses of this type of convectively influenced CAT when the NWP model accurately forecasts upstream convection.
Significance Statement
In this study we document the role of distant convection on observed widespread strong clear-air turbulence near upper-level jet streams in different weather patterns. Results from nested NWP model simulations, together with similar examples from previous case studies, suggest a strong association of widespread turbulence with jet stream enhancements related to outflow from upstream convection. We also demonstrate how model horizontal grid spacings of <1 km are required to adequately resolve common turbulence onset mechanisms (e.g., Kelvin–Helmholtz instability, gravity wave breaking). Nevertheless, examples are provided showing that turbulence forecasting systems driven by lower-resolution operational NWP models can provide potentially valuable guidance on these widespread turbulence events when those models accurately forecast the timing and locations of upstream convection.
Abstract
At 1818 mountain standard time 20 December 2008, a Boeing 737 jetliner encountered significant crosswinds while accelerating for takeoff at the Denver International Airport (DIA), ran off the side of the runway, and burst into flames. Passengers and crew were able to evacuate quickly, and, although there were injuries, there were no fatalities. Winds around the time of the accident were predominantly from the west, with substantial spatial and temporal speed variability across the airport property. Embedded in this mostly westerly flow were intermittent gusts that created strong crosswinds for the north–south runways. According to the report from the National Transportation Safety Board, it was one of these strong gusts that initiated the events that led to the runway excursion and subsequent crash of the aircraft. Numerous aircraft reported significant mountain-wave activity and turbulence over Colorado on the day of the accident. To determine whether wave activity may have contributed to the strong, intermittent gustiness at DIA, a high-resolution multinested numerical simulation was performed using the Clark–Hall model, with a horizontal grid spacing of 250 m in the inner domain. Results from this simulation suggest that the surface gustiness at DIA was associated with undulations in a train of lee waves in a midtropospheric stable layer above the airport, creating regions of higher-velocity air descending toward the surface. In contrast, a simulation with horizontal grid spacing that was similar to that of a state-of-the-art operational forecast model (3 km) did not predict strong winds at DIA.
Abstract
At 1818 mountain standard time 20 December 2008, a Boeing 737 jetliner encountered significant crosswinds while accelerating for takeoff at the Denver International Airport (DIA), ran off the side of the runway, and burst into flames. Passengers and crew were able to evacuate quickly, and, although there were injuries, there were no fatalities. Winds around the time of the accident were predominantly from the west, with substantial spatial and temporal speed variability across the airport property. Embedded in this mostly westerly flow were intermittent gusts that created strong crosswinds for the north–south runways. According to the report from the National Transportation Safety Board, it was one of these strong gusts that initiated the events that led to the runway excursion and subsequent crash of the aircraft. Numerous aircraft reported significant mountain-wave activity and turbulence over Colorado on the day of the accident. To determine whether wave activity may have contributed to the strong, intermittent gustiness at DIA, a high-resolution multinested numerical simulation was performed using the Clark–Hall model, with a horizontal grid spacing of 250 m in the inner domain. Results from this simulation suggest that the surface gustiness at DIA was associated with undulations in a train of lee waves in a midtropospheric stable layer above the airport, creating regions of higher-velocity air descending toward the surface. In contrast, a simulation with horizontal grid spacing that was similar to that of a state-of-the-art operational forecast model (3 km) did not predict strong winds at DIA.
