Title: Statistics of geophysical waves formed by the background fluid flow

Abstract: The waves generated from different sources (ocean surface, topography, tides and ...) are found ubiquitously in the atmosphere and ocean. Once generated, these waves are scattered through advection and refraction by slowly moving background flow. We show this phenomenon in wavenumber space can be described by a diffusion of wave energy on a double cone, a geometry that is uniquely set by the wave frequency. We derive the corresponding diffusion equation and relate its diffusivity to the wave characteristics and the energy spectrum of the randomised background flow. We check the predictions of this equation against numerical simulations of the three-dimensional Boussinesq equations in initial-value and forced scenarios with horizontally isotropic wave and flow fields. In the forced case, wavenumber diffusion results in a wave energy spectrum that scales with k^-2 (k being the wavenumber), which is consistent with as-yet-unexplained features of observed atmospheric and oceanic spectra.