John Craske

Reversibility, mixing and energetics in stratified turbulence via probability distributions.

Flows that are driven or inhibited by density differences are found in a wide variety of settings, including the ocean, the atmosphere and built environments. To quantify how much potential energy can in principle be converted into kinetic energy in such flows, one often uses the concept of 'available potential energy'. I will describe a decomposition of available potential energy into two non-negative components. The 'inner' component accounts for potential energy that can be released within a control volume, while the 'outer' component accounts for possible interactions between the control volume and its surroundings. This decomposition resembles Bayes’ theorem for conditional probabilities and has properties analogous to entropy inequalities from statistical mechanics. Building on this perspective, I will discuss the behaviour of joint probability distributions of multicomponent flow variables, viewed as random
samples drawn from a control volume. The evolution of these distributions is governed by a Fokker–Planck-like equation, which highlights the roles of reversible and irreversible processes in a suitably projected phase space.