An asymptotic theory for the generation of nonlinear surface gravity waves by turbulent air flow. (English) Zbl 0883.76015
Based on a previous linear theory, turbulent air flow over a surface gravity wave of finite amplitude is studied analytically by the methods of matched asymptotic expansions and multiple-scale analysis. In particular, an initial-value problem for weakly nonlinear waves is solved, where the initial conditions are prescribed by a single Stokes wave, displacing the water surface. The water is inviscid and incompressible, and there is no mean shear current. Wave-wave interactions are not taken into account. The validity of the theory is restricted to slow waves and small drag coefficient.
MSC:
76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
86A10 | Meteorology and atmospheric physics |
86A05 | Hydrology, hydrography, oceanography |
Keywords:
matched asymptotic expansions; multiple-scale analysis; initial-value problem; Stokes wave; slow waves; small drag coefficientReferences:
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