Exact coherent states in a quasi-linear model of strongly stratified Kolmogorov flow

Strongly stratified turbulent flows are characterized by sufficiently large values of the Reynolds number Re that the buoyancy Reynolds number Re_b ≡ Re Fr² > 30 (or more) as the Froude number Fr-->0.  In this extreme parameter regime, the flow is dominated by highly anisotropic structures that have horizontal scales much larger than their vertical scales.  Owing to their relative horizontal motion, these structures are susceptible to stratified shear instabilities that drive spectrally non-local energy transfers.  A quasi-linear (QL) model that captures these features of strongly stratified shear flows is derived via asymptotic analysis of the non-rotating Boussinesq equations.  The model is used to investigate the mixing efficiency of certain exact coherent states (ECS) in strongly stratified 2D Kolmogorov (i.e. sinusoidally-forced) flow. The ECS are computed using a new methodology for numerically integrating multiple time-scale QL systems strictly on the "slow" time scale of the mean flow.