Publicação: Green-Naghdi dynamics of surface wind waves in finite depth
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The Miles' quasi laminar theory of waves generation by wind in finite depth h is presented. In this context, the fully nonlinear Green-Naghdi model equation is derived for the first time. This model equation is obtained by the non perturbative Green-Naghdi approach, coupling a nonlinear evolution of water waves with the atmospheric dynamics which works as in the classic Miles' theory. A depth-dependent and wind-dependent wave growth γ is drawn from the dispersion relation of the coupled Green-Naghdi model with the atmospheric dynamics. Different values of the dimensionless water depth parameter δ = gh/U 1, with g the gravity and U 1 a characteristic wind velocity, produce two families of growth rate γ in function of the dimensionless theoretical wave-age c 0: a family of γ with h constant and U 1 variable and another family of γ with U 1 constant and h variable. The allowed minimum and maximum values of γ in this model are exhibited.
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Miles mechanism, nonlinear Green-Nagdhi model, surface waves, waves in finite depth, wind-waves
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Inglês
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Fluid Dynamics Research, v. 50, n. 2, 2018.
