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The Destabilizing Effect of the Ground on Kelvin-Helmholtz Waves in the Atmosphere

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  • 1 Department of Mechanical Engineering Sciences, Wayne State University, Detroit, Mich. 48202
  • | 2 Cooperative Institute for Research in Environmental Sciences, University of Colorado/NOAA and Aeronomy Laboratory, NOAA, Boulder, Colo. 80302
  • | 3 Cooperative Institute for Research in Environmental Sciences, University of Colorado/NOAA, Boulder, Colo. 80302
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Abstract

The simple Kelvin-Helmholtz model for shear zones in the atmosphere is modified, by introducing a solid boundary below to account for the effect of the ground. The new characteristics of neutral and unstable waves that can exist in such configuration are analyzed for various values of wind velocity, depth of the bottom layer, and Brunt-Väisälä frequency. It is shown that the presence of the ground considerably destabilizes waves with long horizontal wavelengths. In particular, long wavelengths are always unstable, so that no neutral stability boundary exists. Furthermore, the solid lower boundary introduces an infinite number of neutral modes, all of which correspond to evanescent waves in the top layer. Finally, the model with the ground is used to calculate the characteristics of the most unstable waves that would be generated for some well-documented observed cases and the calculated values are found to be in reasonable agreement with observations.

Abstract

The simple Kelvin-Helmholtz model for shear zones in the atmosphere is modified, by introducing a solid boundary below to account for the effect of the ground. The new characteristics of neutral and unstable waves that can exist in such configuration are analyzed for various values of wind velocity, depth of the bottom layer, and Brunt-Väisälä frequency. It is shown that the presence of the ground considerably destabilizes waves with long horizontal wavelengths. In particular, long wavelengths are always unstable, so that no neutral stability boundary exists. Furthermore, the solid lower boundary introduces an infinite number of neutral modes, all of which correspond to evanescent waves in the top layer. Finally, the model with the ground is used to calculate the characteristics of the most unstable waves that would be generated for some well-documented observed cases and the calculated values are found to be in reasonable agreement with observations.

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