The evolution of wind-induced ocean waves is studied theoretically. The modeling assumes that wave groups evolve independently of each other in a state of local equilibrium between wind-pumping- and wave-breaking-induced dissipation. The well-known fetch and duration laws appear as natural solutions of the model in the case of a constant wind speed. The link between the fetch and duration laws is explained, and the results are successfully validated against various experimental data.
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E. Fontaine (2012) studied this question.
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