Dr. Remi Tailleux
An outstanding practical challenge in the study of turbulent stratified fluids is to identify a suitable coarse-graining strategy to derive filtered equations of motion that retain only the temporal and numerical scales amenable to direct numerical simulations. To that end, some of the most well known approaches have been those based on Reynolds averaging or on Large-Eddy Simulations (LES). Mathematically, these approaches require a ``turbulent closure'' in order to close the system of equations for the averaged quantities, which would be otherwise ill-posed. Physically, a turbulent closure is essentially an informed guess at the form and structure of certain correlation between fluctuating quantities. A turbulent closure often involves tunable parameters that are usually constrained by experimental data, rarely from first principles arguments. One particularly popular turbulent closure of historical and practical importance assumes that some turbulent fluxes can be expressed as being down the gradient of one of the averaged quantity. The purpose of this talk will be to discuss the validity of downgradient turbulent closures in the light of re-arrangement theory, which allows for a rigorous separation between the reversible effects of stirring and the irreversible effects of mixing. These ideas will be illustrated by means of examples drawn from geophysical fluid dynamicss, pertaining to turbulent mixing in stratified fluids, double diffusion, and potential vorticity mixing in two-dimensional barotropic flows.