Swell refraction by oceanic currents and multiscale stochastic closures

Swell systems are collimated wave groups travelling rapidly across oceanic basins. Along this propagation, waves are refracted by oceanic currents gradients. The small-scale structures of these currents are the key players but are hardly observed by satellite or simulated globally. For this reason, we propose several stochastic closures to simulate the dynamics of waves, and eventually to facilitate future ensemble-based data assimilation algorithms.To model the unresolved mesoscale currents, we propose a random Gaussian process multi-scale in space and time, built on self-similarity arguments. This leads to a non-Markovian closure suitable for our wave-turbulence interaction simulations.For the submesoscale dynamics, Markovian approaches -- e.g., dynamics under Location Uncertainty (LU) or Stochastic Advection by Lie Transport (SALT) -- applied in the wave frame. Under certain assumptions, we found an analytical formula for the probability distribution of wave properties (wave vector, frequency and amplitude) at long time