The catalytic role of beta effect in barotropization processes

Abstract

The vertical structure of freely evolving, continuously stratified, quasi-geostrophic flow is investigated. We predict the final state organization, and in particular its vertical structure, using statistical mechanics and these predictions are tested against numerical simulations. The key role played by conservation laws in each layer, including the fine-grained enstrophy, is discussed. In general, the conservation laws, and in particular that enstrophy is conserved layer-wise, prevent complete barotropization, i.e., the tendency to reach the gravest vertical mode. The peculiar role of the $\beta$-effect, i.e. of the existence of planetary vorticity gradients, is discussed. In particular, it is shown that increasing $\beta$ increases the tendency toward barotropization through turbulent stirring. The effectiveness of barotropisation may be partly parameterized using the Rhines scale $2\pi E_0^{1/4}/{\beta }^{1/2}$. As this parameter decreases (beta increases) then barotropization can progress further, because the beta term provides enstrophy to each layer.

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• A statistical mechanics approach to mixing in stratified fluids
• Equilibrium statistical mechanics and energy partition for the shallow water model
• Ribbon Turbulence
• Nonlinear energy transfers and phase diagrams for geostrophically balanced rotating--stratified flows
• An Introduction to Large Deviations and Equilibrium Statistical Mechanics for Turbulent Flows
• Normal modes with boundary dynamics in geophysical fluids
• Wave turbulence in the two-layer ocean model