Abstract

Stratified shear flows, where the `background’ velocity and density distribution vary over some characteristic length scales, are ubiquitous in the atmosphere and the ocean. At sufficiently high Reynolds number, such flows are commonly believed to play a key role in the transition to turbulence, and hence to be central to irreversible mixing of the density field. Parameterizations of such irreversible mixing within larger scale models of the ocean in particular is a major area of uncertainty, not least because there is a wide range of highly scattered and apparently inconsistent experimental and observational data. Here, I review some of the recent progress using modern mathematical techniques in developing understanding of instability, transition, turbulence and mixing in stratified shear flows, I focus in particular on the crucial role of so-called `exact coherent states’, i.e. unstable solutions of the underlying governing equations which nevertheless appear to play the role of an underlying organising `skeleton’ for turbulent flow dynamics in stratified shear flows.