We adapt the microcanonical framework of equilibrium statistical mechanics to predict the statistics of short linear 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 root-mean-square surface elevation and interfacial slope against numerical simulations.

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• Hydrodynamic waves
• Wave chaos