A universal bifurcation mechanism arising from progressive hydroelastic waves

作     者：Zhan Wang Zhan Wang

作者机构：Institute of MechanicsChinese Academy of SciencesBeijing 100190China School of Engineering ScienceUniversity of Chinese Academy of SciencesBeijing 100049China 

出 版 物：《Theoretical & Applied Mechanics Letters》 (力学快报（英文版）)

年 卷 期：2022年第12卷第1期

页      面：23-29页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China under Grant No.11772341 the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDB22040203 

主　　题：Nonlinear wave Supercritical bifurcation Hydroelastic wave Wavepacket 

摘      要：A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic nonlinearities, is an extension of the famous Whitham equation. The coefficients of the nonlinear terms are chosen to match with the key properties of the full Euler equations, precisely, the associated cubic nonlinear Schrödinger equation and the amplitude of the solitary wave at the bifurcation point. It is shown that the supercritical bifurcation, rich with Stokes, solitary, generalized solitary, and dark solitary waves in the vicinity of the phase speed minimum, is a universal bifurcation mechanism. The newly developed model can capture the essential features near the bifurcation point and easily be generalized to other nonlinear wave problems in hydrodynamics.