Laboratoire
d'Hydrodynamique

Density stratified fluids are everywhere: the oceans; the atmosphere; and many, many industrial processes involve fluids subject to gravity where the density is not constant.
How such fluids mix is of great topical interest, as the parameterisation of stratified mixing on the small-scale is a key component of larger-scale global climate models.
However, particularly when the flow is turbulent, the energetics of such mixing is subtle. If the fluid is stably stratified, with dense fluid beneath lighter fluid,  mixing will tend to lift the centre of mass, and hence increase the potential energy of the system. Therefore, the kinetic energy in the `forcing' of the turbulent flow must be partitioned between turbulent dissipation and potential energy gain, and a central challenge for models is to describe the `efficiency' of stratified mixing, ie the fraction of the forcing input energy which increases (irreversibly) the system's potential energy.  It is intuitively appealing to suppose that `strong' stratification will tend to suppress vertical motions, and hence reduce, or even entirely suppress,  stratified mixing. A conventional way to describe this assumed dependence of mixing on the strength of stratification is in terms of some kind of a  `Richardson number', which may be thought of loosely as a ratio of  possible potential energy change of the system to a measure of the system's kinetic energy (often associated with shear). Conventional models assume mixing switches off at sufficiently high Richardson number, when there is apparently not enough energy available to `overturn' and hence mix relatively dense and buoyant fluid. In this talk, I present recent experimental and observational evidence which both suggest that strongly stratified fluids can continue to mix efficiently through repeated `scouring' of wisps of dense fluid by turbulent eddies. I discuss the implications of this evidence for the parameterisation of stratified mixing, modifying and reinterpreting a strangely neglected, yet highly relevant, model originally proposed by Stuart Turner over 40 years ago.