Nonlinear evolution of optimal perturbations to strongly stratified shear layers

Abstract eng:
Vertical mixing in the stably-stratified ocean interior is often assumed to arise due to shear instabilities. However, there is observational, experimental, and numerical evidence that suggests increased dissipation may also occur in more strongly stratified flows. The non-normality of the Navier-Stokes and buoyancy equations may allow for substantial perturbation energy growth at finite times, even in flows which are stable in the Miles-Howard sense. Here we show that this transient growth mechanism may be sufficient to trigger strongly nonlinear effects and breakdown into small-scale structures, thereby leading to enhanced dissipation and non-trivial modification of the background flow. The effects of nonlinearity are felt more strongly for higher Re and lower Rib . As such, this may point to transient non-normal growth as a possible linear mechanism to trigger turbulence and mixing in stably-stratified shear flows.

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