The catalytic role of beta effect in barotropization processes

TL;DR

This paper investigates how planetary vorticity gradients (beta effect) influence the vertical organization of stratified geophysical flows, showing that increasing beta promotes barotropization through turbulent stirring and enstrophy transfer.

Contribution

It reveals the catalytic role of the beta effect in enhancing barotropization by providing enstrophy, supported by statistical mechanics predictions and numerical simulations.

Findings

Increasing beta enhances barotropization tendency.

Conservation laws prevent complete barotropization.

The Rhines scale parameterizes barotropization effectiveness.

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.