Is spontaneous generation of coherent baroclinic flows possible?

Geophysical turbulence is observed to self-organize into large-scale flows such as zonal jets and coherent vortices. Previous studies on barotropic beta-plane turbulence have shown that coherent flows emerge out of a background of homogeneous turbulence as a bifurcation when the turbulence intensity increases and the emergence of large scale flows has been attributed to a new type of collective, symmetry breaking instability of the statistical state dynamics of the turbulent flow. In this work we extend the analysis to stratified flows and investigate turbulent self-organization in a two-layer fluid with no imposed mean north-south thermal gradient and turbulence supported by an external random stirring. We use a second order closure of the statistical state dynamics (S3T) with an appropriate averaging ansatz that allows the identification of statistical turbulent equilibria and their structural stability. The bifurcation of the statistically homogeneous equilibrium state to inhomogeneous equilibrium states comprising of zonal jets and/or large scale waves when the energy input rate of the excitation passes a critical threshold is analytically studied. The theory predicts that when the flow transitions to a statistical state with large-scale structures, these states are barotropic if the scale of excitation is larger than the deformation radius. Mixed barotropic-baroclinic states with jets and/or waves arise when the excitation is at scales shorter than the deformation radius with the baroclinic component of the flow being subdominant for low energy input rates and non-significant for higher energy input rates. The results of the S3T theory are compared to nonlinear simulations. The theory is found to accurately predict both the critical transition arameters and the scales of the emergent structures but underestimates their amplitude.
Comment: submitted to the Journal of Fluid Mechanics