Journal of Ocean Engineering and Science

Volume 1, Issue 1

(1)Numerical study on the generation and evolution of the super-rogue waves

Jianmin Yang ^a,b, Wenyue Lu ^a,b,∗
^a State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, China
^bCollaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE)
Received 6 July 2015; received in revised form 8 September 2015; accepted 27 September 2015
Available online 29 January 2016

Abstract
The super-rogue wave solutions of the nonlinear Schrödinger equation (NLS) are numerically studied based on the weakly nonlinear hydrodynamic equation. The super-rogue wave solutions up to the 5th order, also known as the so-called super-rogue waves, are observed according to the results obtained by numerically solving the modified nonlinear Schrödinger equation which is also known as the Dysthe equation that has a higher accuracy along the wave evolution in space. By using the 4th order split-step pseudo-spectral method during the integral process, more accurate results with a smaller conservation error were obtained. It is found that the super-rogue waves can be generated when considering the higher order nonlinearity. The fourth-order terms in the mNLS equation should not be ignored in numerically simulating the evolution of the super-rogue wave formation. The bound wave components also play important roles in the wave evolution. The enhancement of wave amplitude becomes larger due to the influence of bound wave components.
© 2016 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Super-rogue wave; Nonlinear Schrödinger equation; mNLS; Rational solutions.