Abstract

Parameterizing the mixing of a stratified fluid is a fundamental challenge for models of environmental and industrial flows. In particular, it is of great value to parameterize the efficiency of turbulent mixing, in the sense of the proportion of the kinetic energy converted into potential energy (through irreversible mixing of fluid of varying density) compared to the total amount of energy converted into potential energy and internal energy (through irreversible viscous dissipation). In this talk I review experimental, numerical and observational evidence which has lead to the development of various competing models for the dependence of mixing on the overall stratification. In an attempt to reconcile the differences between these models and measurements, I present a novel theoretical approach based around generating rigorous bounds on the mixing rate through imposing various reasonable physical constraints in a model (though applicable) variational problem.