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Directional diffusion of surface gravity wave action by ocean macroturbulence

TitleDirectional diffusion of surface gravity wave action by ocean macroturbulence
Publication TypeJournal Article
Year of Publication2020
AuthorsBoas A.BV, Young W.R
Date Published2020/05
Type of ArticleArticle
ISBN Number0022-1120
Accession NumberWOS:000525740100001
Keywordsair/sea interactions; currents; dispersion; mechanics; motions; physics; refraction; scale; surface gravity waves; swell; water; waves in random media

We use a multiple-scale expansion to average the wave action balance equation over an ensemble of sea-surface velocity fields characteristic of the ocean mesoscale and submesoscale. Assuming that the statistical properties of the flow are stationary and homogeneous, we derive an expression for a diffusivity tensor of surface-wave action density. The small parameter in this expansion is the ratio of surface current speed to gravity wave group speed. For isotropic currents, the action diffusivity is expressed in terms of the kinetic energy spectrum of the flow. A Helmholtz decomposition of the sea-surface currents into solenoidal (vortical) and potential (divergent) components shows that, to leading order, the potential component of the surface velocity field has no effect on the diffusivity of wave action: only the vortical component of the sea-surface velocity results in diffusion of surface-wave action. We validate our analytic results for the action diffusivity by Monte Carlo ray-tracing simulations through an ensemble of stochastic velocity fields.

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