Distinguished Colloquium

In this colloquium talk, I will discuss a number of examples, mainly from stochastic and deterministic fluid mechanics, that evolve to some equilibrium, often a statistical equilibrium. I will contrast different mechanisms that produce this convergence and give intuition about the character of the mechanism. Examples will include stochastically forced fluid mechanics, transport of a passive scalar by an idealized fluid, as well as a new form of Markov Chain Monte Carlo. Along the way, I will make connections to some (hopefully) interesting phenomena, including a proof of Batchelor spectra for a driven system and showing how it fits with Onsager’s predictions of how driven systems evolve to a critical state in the absence of dissipation.