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The Mixing of Mass and Momentum by Kelvin-Helmboltz Billows

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  • 1 Centre for Atmospheric Science, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England
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Abstract

The mixing of mass and momentum induced by the full life cycle of stratified shear instability is considered. In particular, the nonlinear numerical simulation of a stratified shear layer that is unstable to Kelvin–Helmholtz (K–H) waves is undertaken in three spatial dimensions. The numerical experiments are designed to model the secondary convective instability of the K–H billow previously indicated by linear stability analyses and identified in tilted-tank experiments. The initial parallel flows considered in the present study allow for the presence of constant stratification external to the shear layer. For weakly unstable stratified shear layers good agreement is found between the numerical simulations and similar physical (tilted tank) experiments. For strongly unstable stratified shear layers there is less agreement since the final state of the numerical simulations is a long-lived, two-dimensional vortex associated with the primary K–H instability. Quantitative estimates of the efficiency of mixing are made by calculating the flux Richardson number of the modeled mixing events. It is found that the flux Richardson number can strongly depend on the relative strength of the stratification external to the shear layer.

Abstract

The mixing of mass and momentum induced by the full life cycle of stratified shear instability is considered. In particular, the nonlinear numerical simulation of a stratified shear layer that is unstable to Kelvin–Helmholtz (K–H) waves is undertaken in three spatial dimensions. The numerical experiments are designed to model the secondary convective instability of the K–H billow previously indicated by linear stability analyses and identified in tilted-tank experiments. The initial parallel flows considered in the present study allow for the presence of constant stratification external to the shear layer. For weakly unstable stratified shear layers good agreement is found between the numerical simulations and similar physical (tilted tank) experiments. For strongly unstable stratified shear layers there is less agreement since the final state of the numerical simulations is a long-lived, two-dimensional vortex associated with the primary K–H instability. Quantitative estimates of the efficiency of mixing are made by calculating the flux Richardson number of the modeled mixing events. It is found that the flux Richardson number can strongly depend on the relative strength of the stratification external to the shear layer.

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