Mathematics

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 dynamic​​s 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.
​L​ong 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 transfer​s​ 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).​​