A universal bifurcation mechanism arising from progressive hydroelastic waves
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 th...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-01-01
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| Series: | Theoretical and Applied Mechanics Letters |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2095034921001227 |
| _version_ | 1817989226245914624 |
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| author | Zhan Wang |
| author_facet | Zhan Wang |
| author_sort | Zhan Wang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T00:44:29Z |
| format | Article |
| id | doaj.art-96e13794586a4450b32a6ab14acfcb8c |
| institution | Directory Open Access Journal |
| issn | 2095-0349 |
| language | English |
| last_indexed | 2024-04-14T00:44:29Z |
| publishDate | 2022-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Theoretical and Applied Mechanics Letters |
| spelling | doaj.art-96e13794586a4450b32a6ab14acfcb8c2022-12-22T02:22:05ZengElsevierTheoretical and Applied Mechanics Letters2095-03492022-01-01121100315A universal bifurcation mechanism arising from progressive hydroelastic wavesZhan Wang0Corresponding author.; Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, ChinaA 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.http://www.sciencedirect.com/science/article/pii/S2095034921001227Nonlinear waveSupercritical bifurcationHydroelastic waveWavepacket |
| spellingShingle | Zhan Wang A universal bifurcation mechanism arising from progressive hydroelastic waves Theoretical and Applied Mechanics Letters Nonlinear wave Supercritical bifurcation Hydroelastic wave Wavepacket |
| title | A universal bifurcation mechanism arising from progressive hydroelastic waves |
| title_full | A universal bifurcation mechanism arising from progressive hydroelastic waves |
| title_fullStr | A universal bifurcation mechanism arising from progressive hydroelastic waves |
| title_full_unstemmed | A universal bifurcation mechanism arising from progressive hydroelastic waves |
| title_short | A universal bifurcation mechanism arising from progressive hydroelastic waves |
| title_sort | universal bifurcation mechanism arising from progressive hydroelastic waves |
| topic | Nonlinear wave Supercritical bifurcation Hydroelastic wave Wavepacket |
| url | http://www.sciencedirect.com/science/article/pii/S2095034921001227 |
| work_keys_str_mv | AT zhanwang auniversalbifurcationmechanismarisingfromprogressivehydroelasticwaves AT zhanwang universalbifurcationmechanismarisingfromprogressivehydroelasticwaves |