Horizontal shear in the rotating, stratified ocean : Linear theory and nonlinear evolution

Submesoscale instabilities and mixing are poorly understood. We focus our work on barotropic shear with Rossby and Froude numbers of O (1). Instabilities and nonlinear cascades are possible in this regime even though stable stratification is significant. We have demonstrated previously (Arobone and Sarkar, JFM 2012) that the linear stability of the shear layer shows new aspects for strong stratification and moderate rotation rates. In this regime stratification acts to stabilize the inertial instability but greatly increase the range of vertical wavenumbers unstable to barotropic instability when Ro ∼ −1.

Nonlinear simulations are used to explore the shear layer with Ro(t). Coherent structure evolution varies greatly between cases with different moderate anticyclonic values of Ro0, but cyclonic rotation and strong anticyclonic rotation modify the flow in a more straightforward manner. Possible instability mechanisms, e.g. elliptic, zigzag, inertial, and barotropic instabilities are related to the simulation results. Enstrophy budgets from the simulations show a marked transition corresponding to sign reversal of centerline absolute vorticity, consistent with the linear modification of barotropic instability when Ro ∼ −1. New results analyzing saturation of inertial instability in the presence of strong stratification will be presented, noting strong differences from unstratified flows.

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