HAM Solution of Nonlinear Wave Interaction With Uniform Current

Abstract

The interaction of nonlinear progressive waves and uniform currents in water of finite depth is investigated analytically by means of the homotopy analysis method (HAM). In the HAM, the velocity potential of the wave is expressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by continuous mapping. The present approach does not depend on any small parameters, thus the solutions are suitable for steep waves and strong currents. To verify the HAM solutions, experiments are conducted in wave-current flume of Education Ministry Key Laboratory of Hydrodynamics at SJTU. It is shown that the HAM solutions are in good agreement with experimental measurements. The present study demonstrated that the great potential of the HAM to solve more complex wave-current interaction problems leading to engineering applications in traditional offshore industry and marine renewable energy sector.