Stream function representation of nonlinear ocean waves

Abstract

An analytical stream function expression representing a nonlinear gravity water wave is applied both to the representation of measured wave forms and also to nonlinear theoretical waves. The stream function form is chosen so that it is a solution to the Laplace equation and the bottom boundary condition; the parameters in the stream function expression are chosen by a numerical perturbation procedure that provides a best fit to the kinematic and dynamic free surface boundary conditions. The boundary condition errors associated with the nonlinear stream function representation of four measured wave profiles are compared with estimates of the corresponding errors associated with a linear representation. The stream function method is judged more accurate than a linear method if the wave height is greater than 50% of the breaking height. The stream function method is also applied to represent theoretical waves for which only the wave height and period are available to characterize the wave profile. It is demonstrated that the method represents an improvement over other available nonlinear procedures. The method can be employed to represent wave conditions which include a prescribed uniform steady current and a specified pressure distribution on the free surface.