A universal bifurcation mechanism arising from progressive hydroelastic waves |
| |
Institution: | 1. Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China |
| |
Abstract: | 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. |
| |
Keywords: | |
本文献已被 维普 ScienceDirect 等数据库收录! |
|