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Mild-slope approximation for long waves generated by short waves. (English) Zbl 0951.76015

Summary: The mild-slope approximation has become a popular basis for calculating infinitesimal surface waves on slowly varying depth. It is less restrictive and hence more advantageous than the ray and parabolic approximations for describing diffraction and refraction by bathymetry and/or by complex coastlines. Since its computation involves only two horizontal coordinates, the mild-slope equation is also numerically less demanding than the solution of fully three-dimensional equations for a horizontal area with sides much greater than the typical wavelength. By consideration of nonlinear effects of the second order, we derive the mild-slope approximation for long waves over slowly varying depth, in order to provide a convenient basis for predicting long-period resonance in a large harbor by short-period wind waves.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
86A05 Hydrology, hydrography, oceanography
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