Nonlinear progressive waves in water of finite depth – an analytic approximation

Abstract

An explicit solution using Homotopy Analysis Method (HAM) is developed to describe the nonlinear progressive waves in water of finite depth. The velocity potential of the wave is expressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by continuous mapping. Unlike the perturbation method, the present approach is not dependent on small parameters. Thus solutions are possible for steep waves. Furthermore, a significant improvement of the convergence rate and region is achieved by applying Homotopy-Pad頁pproximants. The calculated wave characteristics of the present solution agree well with previous numerical and experimental results.