Coherent interference and diffraction in random waves

Wave fields traveling through a varying medium (e.g. topography, currents), can develop well-defined focal zones and caustics, where the wave field is highly coherent and wave statistics vary rapidly. However, the presence and evolution of such coherent structures in the wave field are not resolved in a quasi-homogeneous description of the wave field (e.g. the radiative transport equation), and a more general description of the wave statistics (and its evolution) is needed. In this work we demonstrate with numerical examples that, when using a (recently developed) transport equation for the second order inhomeogeneous wave statistics that accounts for cross-variance contributions, we can resolve coherent structures in wave fields such as those typically found in focal and diffraction zones. What this shows is, that in a statistical sense, diffraction is essentially an interference phenomenon that can be readily resolved if cross-phase information in the transport equations is retained.