Numerical Simulation of Rogue Waves Based on the Fourth-Order NLS Equation for Laboratory Experimental Investigation

Abstract

The main purposes of investigating the generation of the rogue waves in offshore engineering include: 1) prediction of its occurrence to protect the offshore structure from attacking; 2) the experimental investigation of rogue waves/structure interaction for the structure design. The latter one calls high requirement of wave generation and calculation. In this paper, we establish a spatial domain model of fourth order nonlinear Schro¨dinger (NLS) equation for describing deep-water wave trains in moving coordinate system. For the first purpose mentioned above, this paper presents the evolution of random wave trains in real sea state described by the Joint North Sea Wave Project (JONSWAP) power spectrum numerically, which is governed by the NLS equation. The parameters of the spectrum are evaluated to discuss their effect on the occurrence of rogue waves. For the second purpose to generate rogue waves in experimental tank efficiently, the transient wave is focused for its allowance of precise determination of concentration place/time. First we simulate the three-dimensional transient waves in the numerical tank modeling the deepwater basin with double-side multi-segmented wave-maker in Shanghai Jiao Tong University (SJTU) with linear superposing theory. To discuss its nonlinearity for the guidance of experiment, the transient wave is set as the initial condition of the NLS equation and the difference from the linear simulation is presented, which could be given as the suggestion to the preparation of experiment.