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Evolution and Breakdown of Kelvin–Helmholtz Billows in Stratified Compressible Flows. Part II: Instability Structure, Evolution, and Energetics

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  • 1 Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado
  • | 2 Norwegian Defense Research Establishment, Kjeller, Norway
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Abstract

A companion paper by Fritts et al. employed a nonlinear, compressible, spectral collocation code to examine the effects of secondary instability on the evolution of Kelvin–Helmholtz billows in stratified shear flows at intermediate Reynolds numbers. The purpose of this paper is to examine the structure, sources, evolution, and energetics of the secondary instability itself. It is found that this instability comprises counterrotating vortices aligned largely along the two-dimensional velocity field (with spanwise wavenumber), with initial instability occurring in the stably stratified braids between adjacent billows and thereafter in the billow cores as maximum KH amplitudes are achieved. The more energetic secondary instabilities are confined to the billows, where the major sources of instability energy are buoyancy and shear due to negative stratification and the solenoidal generation of negative spanwise vorticity within the billow cores. Strain also represents a significant source of streamwise eddy vorticity, with the dominant contribution due to vertical shear within the KH billow acting on vertical eddy vorticity. The authors find that the instability contributes significant fluxes of heat and momentum that act to stabilize the billow structures and advance the restratification at later times. The instability structure within the billows is closely related to that observed in breaking gravity waves and can be viewed as arising due to convective and inertials instability of the evolving two-dimensional flow.

Abstract

A companion paper by Fritts et al. employed a nonlinear, compressible, spectral collocation code to examine the effects of secondary instability on the evolution of Kelvin–Helmholtz billows in stratified shear flows at intermediate Reynolds numbers. The purpose of this paper is to examine the structure, sources, evolution, and energetics of the secondary instability itself. It is found that this instability comprises counterrotating vortices aligned largely along the two-dimensional velocity field (with spanwise wavenumber), with initial instability occurring in the stably stratified braids between adjacent billows and thereafter in the billow cores as maximum KH amplitudes are achieved. The more energetic secondary instabilities are confined to the billows, where the major sources of instability energy are buoyancy and shear due to negative stratification and the solenoidal generation of negative spanwise vorticity within the billow cores. Strain also represents a significant source of streamwise eddy vorticity, with the dominant contribution due to vertical shear within the KH billow acting on vertical eddy vorticity. The authors find that the instability contributes significant fluxes of heat and momentum that act to stabilize the billow structures and advance the restratification at later times. The instability structure within the billows is closely related to that observed in breaking gravity waves and can be viewed as arising due to convective and inertials instability of the evolving two-dimensional flow.

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