Effects of High-Order Nonlinearities on Freak Wave Generation in Random Sea States

Abstract

High-order nonlinearities may be an important cause of freak wave generation; however, it is still unclear how to stimulate the generation of freak waves in deep-water random waves. This study employs the modified fourth-order nonlinear Schrӧdinger equation (mNLSE) to simulate the occurrence of freak waves and analyses the influence of high-order nonlinearities on the evolution of random wave trains described initially by the JONSWAP spectrum. In the evolution of freak wave generation, variations in the linear and nonlinear terms of the mNLSE are displayed with the nonlinear growth of surface elevations. For comparison, the corresponding results from the cubic nonlinear Schrӧdinger equation (CSE) and the linear Schrӧdinger equation (LSE) are also obtained. Power spectra and spectral peakedness curves in the evolution of the wave train are also given to analyze the potential mechanism of freak wave formation. Additionally, the probabilities of freak wave appearances are estimated for different initial parameters and different governing equations. The results show that the fourth-order nonlinearity plays an important role in the generation of freak waves, but this single factor is not enough to generate freak waves, and freak wave occurrence is the contribution of multiple factors to the unstable evolution of the wave train. The higher-order nonlinearity, concentrated initial random phases, larger wave steepness, narrower initial spectral width, and smaller sideband instability parameter can increase the probability of freak wave generation.

Keywords

• freak waves
• high-order nonlinearity
• mnlse
• cse
• lse
• random waves