Equilibrium statistical mechanics of waves in inhomogeneous moving media

Abstract

We adapt the microcanonical framework of equilibrium statistical mechanics to predict the statistics of short waves in inhomogeneous moving media. For steady inhomogeneities and background flow, we compute the wave spectrum at any location in the domain based on an ergodic prescription for the action density in phase space, constrained by conservation of absolute frequency. We illustrate the method for shallow-water waves subject to a background flow or to topographic inhomogeneities, and for deep-water surface capillary waves over a background flow, validating the predicted maps of rms surface elevation and interfacial slope against numerical simulations.