NONLINEAR EVOLUTION-EQUATIONS FOR 2-DIMENSIONAL SURFACE-WAVES IN A FLUID OF FINITE DEPTH

Two-dimensional weakly nonlinear surface gravity-capillary waves in an ideal fluid of finite water depth are considered and nonlinear evolut ion equations which are correct up to the third order of wave steepnes s are derived including the applied pressure on the free surface. Sinc e no assumptions are made on the length scales, the equations can be a pplied to a fluid of arbitrary depth and to disturbances with arbitrar y wavelength. For one-dimensional gravity waves, these evolution equat ions are reduced to those derived by Matsuno (1992). Most of the known equations for surface waves are recovered from the new set of equatio ns as special cases. It is shown that one set of equations has a Hamil tonian formulation and conserves mass, momentum and energy. The analys is for irrotational flow is extended to two-dimensional uniform shear flow.