Effects of Dissipation on Parallel Shear Instability near the Ground

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Abstract
The model used by Davis and Peltier (1976) to study the linear stability of a compressible, stratified parallel shear flow underlain by a rigid boundary is extended to include the effects of turbulent dissipation. It is shown that the incorporation of both eddy viscosity and thermal diffusivity removes the critical level singularity that occurs in the inviscid compressible model. Both Kelvin-Helmholtz and resonant instabilities continue to exist in the presence of dissipation. The stability characteristics of both modal types' are investigated as functions of the parameters of the background flow, including Reynolds number. Dissipation is found to reduce the range of horizontal wavenumbers for which Kelvin-Helmholtz instability is possible, primarily by stabilizing the short-wavelength disturbances. The dissipative resonant modes are also found over a reduced range of parameter space, but the entire region of resonant instability is shifted to shorter horizontal wavelengths. This behavior is expl... Abstract The model used by Davis and Peltier (1976) to study the linear stability of a compressible, stratified parallel shear flow underlain by a rigid boundary is extended to include the effects of turbulent dissipation. It is shown that the incorporation of both eddy viscosity and thermal diffusivity removes the critical level singularity that occurs in the inviscid compressible model. Both Kelvin-Helmholtz and resonant instabilities continue to exist in the presence of dissipation. The stability characteristics of both modal types' are investigated as functions of the parameters of the background flow, including Reynolds number. Dissipation is found to reduce the range of horizontal wavenumbers for which Kelvin-Helmholtz instability is possible, primarily by stabilizing the short-wavelength disturbances. The dissipative resonant modes are also found over a reduced range of parameter space, but the entire region of resonant instability is shifted to shorter horizontal wavelengths. This behavior is expl...

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