Numerical Investigation on Higher-Order Harmonic Waves Induced by a Submerged Inclined Plate

Abstract

In this paper, a two-dimensional time-domain numerical flume has been established to model and investigate nonlinear interactions between nonlinear surface waves and a submerged inclined thin plate. The model solves the Laplace equation and the fully nonlinear free surface boundary conditions within the framework of potential flow theory based on the high-order boundary element method. The mixed Euler–Lagrangian method is applied to update the water surface at each time step, and the fourth-order Runge–Kutta method for time stepping. A so-called four-point method was employed to separate the second-order harmonic free and bounded wave that has the same wave frequency but different wave celerity in front of and behind the submerged plate. It is found that the amplitude of the second-order harmonic free wave increases with the inclination angle of the submerged plate, and the level/amount of the increase is larger for a larger wave steepness. In addition, the amplitudes of both the second-order reflected and transmitted waves are found to increase with the wave steepness, and their empirical relationships are derived for potential use in practical engineering.