A Theory Based on Statistical State Dynamics for the Formation of Jets and Associated Density Layers in Stratified Turbulence

Joseph G. Fitzgerald, Brian F. Farrell

Published 2016-12-10Version 1

Stratified turbulence is characterized by strong anisotropy and a red energy spectrum. Moreover, in many cases the energetic large scales consist of coherent horizontal structures such as vertically sheared horizontal flows, also called stacked jets. Examples of such jets in stratified geophysical flows include the equatorial deep jets in the oceans and the quasi-biennial oscillation in the stratosphere. The mechanism responsible for the formation and maintenance of these jets in stratified turbulence is not fully understood. In this work, the formation and equilibration of coherent turbulent jets is studied using the stochastically excited two-dimensional Boussinesq system. By applying the methods of statistical state dynamics (SSD), we evolve the statistics of the turbulent state forward in time directly, as state variables, rather than obtain them by averaging over realizations of the system. SSD is implemented in the form referred to as S3T, in which the SSD is expressed as a coupled dynamics for the horizontal mean structure and the ensemble mean two-point covariance function of the perturbations from this mean state. The S3T system is shown to reproduce the statistical behaviour, through second order, observed in simulations of the nonlinear Boussinesq dynamics. In particular, S3T captures the spontaneous emergence of jets and density layers in externally-maintained homogeneous turbulence. Analysis of the S3T system is used to explain the jet formation mechanism, the scale selection of the jets, the nonlinear equilibration of the jets, and the dependence of the horizontal mean structure on the stochastic excitation strength.