Stratified Turbulence and the Mesoscale Variability of the Atmosphere

D. K. Lilly National Center for Atmospheric Research, Boulder, CO 80307

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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.

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