The catalytic role of the beta effect in barotropization processes

Abstract

AbstractThe 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$\ensuremath{\beta} $effect, i.e. of the existence of planetary vorticity gradients, is discussed. In particular, it is shown that increasing$\ensuremath{\beta} $increases the tendency toward barotropization through turbulent stirring. The effectiveness of barotropization may be partially parameterized using the Rhines scale$2\lrm{\pi} { E}_{0}^{1/ 4} / {\ensuremath{\beta} }^{1/ 2} $. As this parameter decreases ($\ensuremath{\beta} $increases) then barotropization can progress further, because the$\ensuremath{\beta} $term provides enstrophy to each layer. However, if the$\ensuremath{\beta} $effect is too large then the statistical mechanical predictions fail and wave dynamics prevent complete barotropization.