Is spontaneous generation of coherent baroclinic flows possible?

Abstract

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, a simple model that retains the basic self-organization dynamics, 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 parameters and the scales of the emergent structures but underestimates their amplitude.

Statistical State Dynamics of Weak Jets in Barotropic Beta-Plane Turbulence

“…flows/jets are just emerging with τ e /τ m → 0 (the exactly opposite limit of Bouchet et al (2013)). This perturbative-level agreement is reported by Constantinou et al (2014a); Ioannou (2013a, 2014) for barotropic flows, by Bakas and Ioannou (2018) for baroclinic flows, by Fitzgerald and Farrell (2018a) for vertically sheared stratified flows, by Constantinou and Parker (2018) for magnetized flows in astrophysical settings, and by for the formation of spanwise varying mean flows and mean vortices (streaks-rolls) in 3D channel flows. The reason that the S3T second-order closure works well even for very weak mean flows should be attributed to the existence of the collective flow-forming instability which seems to overpower the disruptive eddyeddy nonlinear interactions, as long as the turbulent intensity is not exceptionally strong (which in most physical situations is usually the case).…”

An Investigation of the Dynamics Leading to the Emergence of Jets and Rossby Waves from a Background of Homogeneous Turbulence in a Baroclinic Atmosphere

“…The manifestation of this instability is the emergence of coherent structures in the turbulent flow. It has been shown that the eigenvectors separate into purely barotropic modes with H = 0 and baroclinic modes with Z = 0 [3]. It was also shown in the same work that the eigenvalues for the barotropic (σ ψ ) and the baroclinic (σ θ ) modes, respectively, satisfy the equations:…”

“…One such model of the baroclinic stably stratified atmosphere is the Phillips two-layer model on a beta-plane with turbulence sustained by random stirring. Numerical simulations of this model have shown that coherent zonal jets and westward-propagating Rossby waves suddenly emerge from the background of the homogeneous turbulent field when a threshold of the energy rate of the stochastic forcing is surpassed [3]. Interestingly, the emerging structures were found to be barotropic for a strong enough stratification, even in cases of mainly exciting baroclinic eddies.…”

“…In order to investigate the fluxes driving the instability, we focus on the parameter regime very close to the stability boundary, that is, when real σ ψ = real(σ θ ) = 0. In this limit, it was shown that the imaginary part of the eigenvalues follow the barotropic and baroclinic Rossby wave dispersion relations, respectively [3], that is:…”