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Vertically banded zonal jets are frequently observed in weakly ornon-rotating stratified turbulence, with the quasi-biennial oscillation in theequatorial stratosphere and the ocean's equatorial deep jets being twoexamples. Explaining the formation of jets in stratified turbulence is afundamental problem in geophysical fluid dynamics. Statistical state dynamics(SSD) provides powerful methods for analyzing turbulent systems exhibitingemergent organization, such as banded jets. In SSD, dynamical equations arewritten directly for the evolution of the turbulence statistics, enablingdirect analysis of the statistical interactions between the incoherentcomponent of the turbulence and the coherent large-scale structure componentthat underlie jet formation. A second-order closure of SSD, known as S3T, haspreviously been applied to show that meridionally banded jets emerge inbarotropic beta-plane turbulence via a statistical instability referred to asthe zonostrophic instability. Two-dimensional Boussinesq turbulence provides asimple model of non-rotating stratified turbulence analogous to the beta-planemodel of planetary turbulence. Jets known as vertically sheared horizontalflows (VSHFs) often emerge in simulations of Boussinesq turbulence, but theirdynamics is not yet clearly understood. In this work S3T analysis of thezonostrophic instability is extended to study VSHF emergence in two-dimensionalBoussinesq turbulence using an analytical formulation of S3T amenable toperturbation stability analysis. VSHFs are shown to form via an instabilitythat is analogous in stratified turbulence to the zonostrophic instability inbeta-plane turbulence. This instability is shown to be strikingly similar tothe zonostrophic instability, suggesting that jet emergence in both geostrophicand non-rotating stratified turbulence may be understood as instances of thesame generic phenomenon.

journal of the atmospheric sciences

Vertically Sheared Horizontal Flow-Forming Instability in Stratified  Turbulence: Analytical Linear Stability Analysis of Statistical State  Dynamics Equilibria