Swell propagation through submesoscale turbulence

Abstract

The propagation of ocean swells from generating regions to remote coastlines is affected by submesoscale turbulence in the surface flow field. The presence of submesoscale velocity variations results in random scattering of wave rays. While the interactions with these flow fields are weak, cumulative effects over oceanic scales are significant and result in observable changes in the wave field. Using geometrical optics and statistical mechanics we derive a framework to express these scattering effects on the mean wave statistics directly in terms of the variance spectrum of the submesoscale current field. The theoretical results are presented in Lagrangian and Eulerian forms, where the latter takes the form of a radiative transport equation augmented with a diffusive term in directional space. The theoretical results are verified through Monte Carlo simulations with a geometrical optics model. We show that including submesoscale scattering on ocean wave evolution can explain observed delays in swell arrivals, accelerated wave height decay, and much larger directional spreading of the wave field than predicted by geometrical spreading alone.