A stochastic parametrization for breaking dynamics of water waves is proposed. The parametrization derives from the analysis of Lagrangian particle paths, from computed and laboratory data. The Langevin dynamics combines a drift term largely informed by deterministic dynamics and a diffusion process that is based upon Matern processes. The data is further analyzed using ellipse ridge analyses, yielding a compact representation of this complex dynamics as well as the clean calculation of the residual flow from progressive multi-chromatic waves.
Long term aims of this work are to derive robust a dispersion models as well as to derive a parametrization and estimates of the dissipation due to breaking on waves and currents. The former is essential to transport dynamics, the latter to the determination of critical momentum transfers between the microscale oscillatory and the macroscale mean flows. Preliminary results of the projection of dissipation in the Lagrangian frame to the Eulerian frame makes this estimate practical in applied oceanography. This is work with Jorge Ramirez (U. Nacional de Colombia), Ken Melville (Scripps/UCSD), and Luc Deike (Princeton).