Layer formation in horizontal stratified Kolmogorov flow

This page accompanies research into coherent structures driving layer formation and mixing in body-forced stably-stratified turbulence. Joint work with C. P. Caulfield and R. R. Kerswell as part of the MUST program.

A preprint of the first paper is available here.

We have also written a follow up paper on the mixing properties of this flow using unstable periodic orbits as proxies for the turbulence, see here for a preprint of the paper and here for movies of the UPOs.

Movies below show total density and streamwise velocity. Using a throttling method to maintain a statistically stationary state and applying a body forcing term sin(y) in the x direction, we find the spontaneous appearance of layers via the inclination of the background shear.

DNS B=2000, D0=250, Re=50 which is case D5 from the table in the paper
DNS B=500, D0=100, Re=75 which is case C1 from the table in the paper

This true “zig-zag” pattern is found as the nonlinear saturated state arising from a sequence of instabilities of the base flow. We converge this unstable steady state using a Newton-GMRES-hookstep algorithm from a guess extracted directly from the chaotic simulation. This is state (C) in the figure above. This solution can be traced in parameter space to construct a bifurcation diagram and we find that the state originates in two separate instabilities, the first of which is a new stratified instability of the base flow, giving rise to state (A).