A consistent phase-averaged model of the interactions between surface gravity waves and currents
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915816595783680 |
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| author | Vanneste, Jacques Young, William R. |
| author_facet | Vanneste, Jacques Young, William R. |
| contents | We formulate a model of the two-way interactions between surface gravity waves and ocean currents. The model couples the transport of wave action in the four-dimensional (horizontal) position--wavevector phase space with the Craik--Leibovich system for the currents. Coupling is via the Doppler shift in the dispersion relation governing action transport, and wave pseudomomentum in the Craik--Leibovich system. The velocity in the Doppler shift is a vertical integral of the Lagrangian mean velocity of the currents, with a weight that is consistent with the vertical structure of the pseudomomentum. This consistency ensures conservation of momentum and energy in the coupled wave--current system.
The conservation properties of the wave--current model stem from an underlying variational structure. We derive this structure from that of the rotating Euler equations for an incompressible fluid with free surface by introducing a Lagrangian wave--mean decomposition, making simplifying approximations, and Whitham averaging.
We apply the wave--current model to the problem of generation of inertial oscillations by surface waves originally considered by Hasselmann. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21976 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A consistent phase-averaged model of the interactions between surface gravity waves and currents Vanneste, Jacques Young, William R. Atmospheric and Oceanic Physics Fluid Dynamics We formulate a model of the two-way interactions between surface gravity waves and ocean currents. The model couples the transport of wave action in the four-dimensional (horizontal) position--wavevector phase space with the Craik--Leibovich system for the currents. Coupling is via the Doppler shift in the dispersion relation governing action transport, and wave pseudomomentum in the Craik--Leibovich system. The velocity in the Doppler shift is a vertical integral of the Lagrangian mean velocity of the currents, with a weight that is consistent with the vertical structure of the pseudomomentum. This consistency ensures conservation of momentum and energy in the coupled wave--current system. The conservation properties of the wave--current model stem from an underlying variational structure. We derive this structure from that of the rotating Euler equations for an incompressible fluid with free surface by introducing a Lagrangian wave--mean decomposition, making simplifying approximations, and Whitham averaging. We apply the wave--current model to the problem of generation of inertial oscillations by surface waves originally considered by Hasselmann. |
| title | A consistent phase-averaged model of the interactions between surface gravity waves and currents |
| topic | Atmospheric and Oceanic Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2602.21976 |