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Wave–Current Interactions in Finite Depth

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  • 1 Scripps Institution of Oceanography, La Jolla, California
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Abstract

The energy, momentum, and mass-flux exchanges between surface waves and underlying Eulerian mean flows are considered, and terms in addition to the classical wave “radiation stress” are identified. The formulation is made in terms of the vertically integrated flow. The various terms are identified with other analyses and interpreted in terms of physical mechanisms, permitting reasonable estimates of the associated depth dependencies. One term is identified with the integrated “CL vortex force” implemented, for example, in simulations of Langmuir circulation. However, as illustrated with a simple example of steady refraction across a shear zone, other terms of the same order can significantly alter the results. The classic example of long waves forced by short-wave groups is also revisited. In this case, an apparent singularity arising in shallow water is countered by finite-amplitude dispersion corrections, these being formally of the same order as the forced long-wave response, and becoming significant or dominant as shallow water is approached.

Corresponding author address: Dr. J. A. Smith, Scripps Institution of Oceanography, UCSD, Mail Stop 0213, 9500 Gilman Dr., La Jolla, CA 92093-0213. Email: jasmith@ucsd.edu

Abstract

The energy, momentum, and mass-flux exchanges between surface waves and underlying Eulerian mean flows are considered, and terms in addition to the classical wave “radiation stress” are identified. The formulation is made in terms of the vertically integrated flow. The various terms are identified with other analyses and interpreted in terms of physical mechanisms, permitting reasonable estimates of the associated depth dependencies. One term is identified with the integrated “CL vortex force” implemented, for example, in simulations of Langmuir circulation. However, as illustrated with a simple example of steady refraction across a shear zone, other terms of the same order can significantly alter the results. The classic example of long waves forced by short-wave groups is also revisited. In this case, an apparent singularity arising in shallow water is countered by finite-amplitude dispersion corrections, these being formally of the same order as the forced long-wave response, and becoming significant or dominant as shallow water is approached.

Corresponding author address: Dr. J. A. Smith, Scripps Institution of Oceanography, UCSD, Mail Stop 0213, 9500 Gilman Dr., La Jolla, CA 92093-0213. Email: jasmith@ucsd.edu

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