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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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Effects of Coexisting Surface Waves on Propagation of a Surface Wave Train
Abstract Spectral surface wave models predict the wave action evolution of multiple wave components. It is well understood that the group speed of the wave action of a particular wave component is modified if an Eulerian near-surface current exists. However, a typical ocean wave field also introduces a significant integrated Stokes drift, or Lagrangian mass transport, and its impact on the group speed of a particular wave component is not well known. In this study, the wave evolution equations are derived in the presence of two wave trains, and the impacts of one wave train on the phase and group speeds of the other wave train are investigated. The results are extended to estimate the impact of the entire wave spectrum on the propagation of a particular wave train. It is found that the group speed of the dominant waves can be significantly enhanced by the presence of other waves, by up to 0.3–0.4 m s−1or 4%–5%, in strongly wind-forced conditions under tropical cyclones. This increase of the group speed is almost twice as large as the advection by a sheared current with the same profile as the Stokes drift integrated over the wave spectrum. Introducing this enhanced group speed in the wave models may make a noticeable impact on their surface wave predictions. It is also found that the increase of the phase speed of a particular wave component is much larger than the advection by a sheared current with the same profile as the integrated Stokes drift.
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- Award ID(s):
- 2048752
- PAR ID:
- 10665403
- Publisher / Repository:
- AMS
- Date Published:
- Journal Name:
- Journal of Physical Oceanography
- Volume:
- 55
- Issue:
- 7
- ISSN:
- 0022-3670
- Page Range / eLocation ID:
- 847 to 863
- Format(s):
- Medium: X
- Associated Dataset(s):
- View Associated Dataset(s) >>
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1175/JPO-D-25-0001.1
