Numerical Generation of Solitary Wave and Its Propagation Characteristics in a Step-Type Flume

Abstract

This work concerns the numerical generation of stable solitary waves by using a piston-type wave maker and the propagation characteristics of a solitary wave in a step-type flume. The numerical generation of solitary waves was performed by solving N-S (Navier–Stokes) equations on the open source CFD (computational fluid dynamics) platform OpenFOAM. To this end, a new module of dynamic boundary conditions was programmed and can be applied to prescribe the horizontal linear motion of a paddle. Two kinds of paddle motions, based on both the first-order and ninth-order solutions of solitary waves, were first determined. The time history of paddle motion was restored in a file, which was then used as an input for the virtual wave maker. The solitary wave in water with a constant depth was generated by both numerical simulation and experiment in the wave flume installed with a piston wave maker. The results show that the amplitudes of trailing waves based on the first-order solution are larger than those based on the ninth-order solution and that wave height based on the first-order solution decays more quickly. The numerical wave profiles are in good agreement with the experimental ones. The propagation characteristics of a solitary wave in a step-type flume was numerically investigated as well. It was found that a part of the solitary wave is reflected when the solitary wave passes the step due to blockage effects, and the forward main wave collapses quickly when it enters shallow water. This work presents a very successful numerical study of stable solitary wave generation and reveals the phenomena when a solitary wave propagates in a step-type flume.

Keywords

• solitary wave
• piston wave maker
• N-S equations
• a step-type flume