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Evolution and Breakdown of Kelvin–Helmholtz Billows in Stratified Compressible Flows. Part I: Comparison of Two- and Three-Dimensional Flows

David C. FrittsLaboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado

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Teresa L. PalmerLaboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado

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Øyvind AndreassenNorwegian Defense Research Establishment, Kjeller, Norway

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Ivar LieNorwegian Defense Research Establishment, Kjeller, Norway

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Abstract

The authors use a nonlinear, compressible, spectral collocation code to examine the evolution and secondary instability of Kelvin–Helmholtz billows in stratified shear flows at intermediate Reynolds numbers. Two-dimensional results exhibit structure consistent with previous numerical studies and suggest dissipation via diffusive transports within the billow cores. Results obtained permitting three-dimensional structures show, in contrast, that secondary instability results in a series of counter-rotating vortices that occupy the outer portions of the billow structures, are oriented in the plane of two-dimensional motion, largely along the two-dimensional velocity field, and contribute substantially to mixing and homogenization of the billow cores at later times. Examination of the flow structure leading to secondary instability also suggests an alternative explanation of the nature of this instability in stratified flows to that offered previously. Comparison of the two-dimensional and spanwise-averaged three-dimensional results reveals that secondary instability contributes large fluxes of momentum and potential temperature, and advances somewhat the restoration of a stratified mean state, but also suggests that secondary instability does not strongly affect the initial two-dimensional evolution for the parameters considered. Though representative of Kelvin–Helmholtz evolutions only under a limited range of flow conditions, our results imply an important role for secondary instability and an inability of two-dimensional studies to describe the dynamics, transports, and mixing in cases where it occurs. The structure, evolution, sources, and energetics of the secondary instability observed in our simulations are the subject of a companion paper by Palmer et al.

Abstract

The authors use a nonlinear, compressible, spectral collocation code to examine the evolution and secondary instability of Kelvin–Helmholtz billows in stratified shear flows at intermediate Reynolds numbers. Two-dimensional results exhibit structure consistent with previous numerical studies and suggest dissipation via diffusive transports within the billow cores. Results obtained permitting three-dimensional structures show, in contrast, that secondary instability results in a series of counter-rotating vortices that occupy the outer portions of the billow structures, are oriented in the plane of two-dimensional motion, largely along the two-dimensional velocity field, and contribute substantially to mixing and homogenization of the billow cores at later times. Examination of the flow structure leading to secondary instability also suggests an alternative explanation of the nature of this instability in stratified flows to that offered previously. Comparison of the two-dimensional and spanwise-averaged three-dimensional results reveals that secondary instability contributes large fluxes of momentum and potential temperature, and advances somewhat the restoration of a stratified mean state, but also suggests that secondary instability does not strongly affect the initial two-dimensional evolution for the parameters considered. Though representative of Kelvin–Helmholtz evolutions only under a limited range of flow conditions, our results imply an important role for secondary instability and an inability of two-dimensional studies to describe the dynamics, transports, and mixing in cases where it occurs. The structure, evolution, sources, and energetics of the secondary instability observed in our simulations are the subject of a companion paper by Palmer et al.

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