Exact coherent structures in two-dimensional strongly stratified Kolmogorov flow

Stably stratified turbulence is a primary agent for diabatic mixing in atmospheric and oceanic flows but occurs on scales that are too small to be resolved in regional circulation much less climate models. In the limit of strong stratification, a highly anisotropic, layer-like horizontal flow develops with emergent vertical shear sufficiently strong to trigger spatially-localized regions of instability. To better understand the spatial structure of these instabilities, their nonlinear saturation, and the diabatic mixing they drive, we employ tools from modern dynamical systems theory. Specifically, we develop a Newton-Krylov iterative solver to compute “exact coherent structures” (ECS), i.e., fully nonlinear, invariant solutions, in the idealized and well-controlled setting of two-dimensional stratified Kolmogorov flow. Unlike prior related studies, we investigate the physically-relevant regime of small Froude and large Reynolds number. We explore the dependence of the numerically computed ECS on these parameters and the domain size, and compare our results with DNS and with predictions from a recently-derived quasilinear reduction of the governing Boussinesq equations in this regime.