Nonlinear waves and solitons in water

A new theoretical model is introduced for evaluating three-dimensional gravity-capillary waves in water of uniform depth to various degrees of validity for predicting nonlinear dispersive water wave phenomena. It is first based on two basic equations, one being the continuity equation averaged over the water depth, and the ether the horizontal projection of the momentum equation at the free surface. These two partial differential equations are both exact (for flows assumed incompressible and inviscid), but involve three unknowns: the horizontal velocity at the free surface (in two horizontal dimensions), (u) over cap; the depth-mean horizontal velocity, (u) over bar; and the water surface elevation, zeta. Closure of the system for modeling fully nonlinear and fully dispersive water waves is accomplished by finding for the velocity field a third exact equation relating these unknowns. Interesting phenomena in various cases are illustrated with review and discussion of literature. Copyright (C) 1998 Published by Elsevier Science B.V.