Nonlinear Wave–Current Interaction in Water of Finite Depth

Abstract

The interaction of nonlinear progressive waves and a uniform current in water of finite depth is investigated analytically by means of the homotopy analysis method (HAM). With HAM, the velocity potential of the flow and the surface elevation are expressed by the Fourier series, and the nonlinear free surface boundary conditions are satisfied by continuous mapping. Unlike a perturbation method, 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 the wave–current flume of the Education Ministry Key Laboratory of Hydrodynamics at Shanghai Jiao Tong University (SJTU) in Shanghai, China. It is found that the HAM solutions are in good agreement with experimental measurements. Based on the series solutions of the validated analytical model, the influence of water depth, wave steepness, and current velocity on the physical properties of the coexisting wave–current field are studied in detail. The variation mechanisms of wave characteristics due to wave–current interaction are further discussed in a quantitative manner. The significant advantage of HAM in dealing with strong nonlinear wave–current interactions in the present study is clearly demonstrated in that the solution technique is independent of small parameters. A comparative study on wave characteristics further reveals the great potential of HAM to solve more complex wave–current interaction problems, leading to engineering applications in the offshore industry and the marine renewable energy sector.