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- Author or Editor: D. K. LILLY x
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Abstract
Abstract
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.
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.
Abstract
Linearized conditional instability theory is used to test the effects of lateral boundary conditions on convective elements. By this theory the outer environment of an amplifying convective element acts like an internal gravity wave with imaginary horizontal wavelength which propagates outward with a wave velocity slightly greater than that of hydrostatic modes. Lateral boundary conditions based on wave radiation principles are therefore appropriate and can eliminate the growth constraints produced by rigid or periodic boundaries.
Abstract
Linearized conditional instability theory is used to test the effects of lateral boundary conditions on convective elements. By this theory the outer environment of an amplifying convective element acts like an internal gravity wave with imaginary horizontal wavelength which propagates outward with a wave velocity slightly greater than that of hydrostatic modes. Lateral boundary conditions based on wave radiation principles are therefore appropriate and can eliminate the growth constraints produced by rigid or periodic boundaries.
Abstract
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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.
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.
The energy and momentum removed from the troposphere and lower atmosphere by the breaking of large amplitude mountain lee waves may be a significant factor in the evolution and maintenance of the large-scale atmospheric circulation. A program is outlined for improving knowledge and understanding of this phenomenon and for incorporating its effects into numerical simulation and forecasting models.
The energy and momentum removed from the troposphere and lower atmosphere by the breaking of large amplitude mountain lee waves may be a significant factor in the evolution and maintenance of the large-scale atmospheric circulation. A program is outlined for improving knowledge and understanding of this phenomenon and for incorporating its effects into numerical simulation and forecasting models.
Abstract
A system is proposed for grid allocation and differencing of apparently general applicability to purely marching-type systems of equations of fluid dynamics. The method is based on casting of the equations into the conservation form, which then permits use of a staggered space-time grid system with interpolations required only in certain linear terms. The method is illustrated by application to two systems of equations, on one of which numerical experiments have been successfully performed. Advantages and drawbacks of the method are described in comparison to other currently used grid systems, and the possibility and desirability of parametric simulation of turbulent eddy exchange processes are discussed.
Abstract
A system is proposed for grid allocation and differencing of apparently general applicability to purely marching-type systems of equations of fluid dynamics. The method is based on casting of the equations into the conservation form, which then permits use of a staggered space-time grid system with interpolations required only in certain linear terms. The method is illustrated by application to two systems of equations, on one of which numerical experiments have been successfully performed. Advantages and drawbacks of the method are described in comparison to other currently used grid systems, and the possibility and desirability of parametric simulation of turbulent eddy exchange processes are discussed.
Abstract
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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.
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.
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.
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.
