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A resonant test-field model of gravity waves

Published online by Cambridge University Press:  20 April 2006

Bruce J. West
Bruce J. West
Affiliation:
Center for Studies of Nonlinear Dynamics, La Jolla Institute, P.O. Box 1434 La Jolla, CA 92038
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Abstract

In this paper we propose an ‘irreversible’ resonant test-field (RTF) model to describe the statistical fluctuations of gravity waves on deep water driven by a turbulent wind field. The non-resonant interactions in the gravity-wave Hamiltonian are replaced by a Markov process in the equation of motion for the resonantly interacting gravity waves, i.e. Hamilton's equations are replaced by a Langevin equation for the RTF waves. The RTF models the irreversible energy-transfer process by a Fokker-Planck equation for the phase-space probability density, the exact steady-state solution of which is determined to be non-Gaussian. An H-theorem for the RTF predicts the monotonic approach to the asymptotic steady state near which the transport properties of the field are studied. The steady-state energy-spectral density is calculated (in some approximation) to be k−4.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 132 , July 1983 , pp. 417 - 430
Copyright
© 1983 Cambridge University Press

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