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Steady state spectral density of gravity-capillary waves

The linear coupling model of Miles and Phillips for the air-sea interaction is generalized to include the average effect of the nonlinear interactions in the dynamic equations for the gravity-capillary waves. The linearized dynamic equations are stochastic with solutions that have stable moments. In particular, a steady state power spectral density for the water wave field is calculated exactly in the context of the model for various wind speeds.