dorsal/arxiv
View SchemaCapillary-gravity wave transport over spatially random drift
| Authors | Guillaume Bal, Tom Chou |
|---|---|
| Categories | |
| ArXiv ID | physics/0001001 |
| URL | https://arxiv.org/abs/physics/0001001 |
Abstract
We derive transport equations for the propagation of water wave action in the presence of a static, spatially random surface drift. Using the Wigner distribution $\W(\x,\k,t)$ to represent the envelope of the wave amplitude at position $\x$ contained in waves with wavevector $\k$, we describe surface wave transport over static flows consisting of two length scales; one varying smoothly on the wavelength scale, the other varying on a scale comparable to the wavelength. The spatially rapidly varying but weak surface flows augment the characteristic equations with scattering terms that are explicit functions of the correlations of the random surface currents. These scattering terms depend parametrically on the magnitudes and directions of the smoothly varying drift and are shown to give rise to a Doppler coupled scattering mechanism. The Doppler interaction in the presence of slowly varying drift modifies the scattering processes and provides a mechanism for coupling long wavelengths with short wavelengths. Conservation of wave action (CWA), typically derived for slowly varying drift, is extended to systems with rapidly varying flow. At yet larger propagation distances, we derive from the transport equations, an equation for wave energy diffusion. The associated diffusion constant is also expressed in terms of the surface flow correlations. Our results provide a formal set of equations to analyse transport of surface wave action, intensity, energy, and wave scattering as a function of the slowly varying drifts and the correlation functions of the random, highly oscillatory surface flows.
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"abstract": "We derive transport equations for the propagation of water wave action in the\npresence of a static, spatially random surface drift. Using the Wigner\ndistribution $\\W(\\x,\\k,t)$ to represent the envelope of the wave amplitude at\nposition $\\x$ contained in waves with wavevector $\\k$, we describe surface wave\ntransport over static flows consisting of two length scales; one varying\nsmoothly on the wavelength scale, the other varying on a scale comparable to\nthe wavelength. The spatially rapidly varying but weak surface flows augment\nthe characteristic equations with scattering terms that are explicit functions\nof the correlations of the random surface currents. These scattering terms\ndepend parametrically on the magnitudes and directions of the smoothly varying\ndrift and are shown to give rise to a Doppler coupled scattering mechanism. The\nDoppler interaction in the presence of slowly varying drift modifies the\nscattering processes and provides a mechanism for coupling long wavelengths\nwith short wavelengths. Conservation of wave action (CWA), typically derived\nfor slowly varying drift, is extended to systems with rapidly varying flow. At\nyet larger propagation distances, we derive from the transport equations, an\nequation for wave energy diffusion. The associated diffusion constant is also\nexpressed in terms of the surface flow correlations. Our results provide a\nformal set of equations to analyse transport of surface wave action, intensity,\nenergy, and wave scattering as a function of the slowly varying drifts and the\ncorrelation functions of the random, highly oscillatory surface flows.",
"arxiv_id": "physics/0001001",
"authors": [
"Guillaume Bal",
"Tom Chou"
],
"categories": [
"physics.flu-dyn",
"physics.ao-ph"
],
"title": "Capillary-gravity wave transport over spatially random drift",
"url": "https://arxiv.org/abs/physics/0001001"
},
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