A fifth-order approximation to gravity-capillary interfacial waves of infinite depth
Two-dimensional periodic gravity-capillary waves at the interface between two unbounded fluids with different density are analyzed. The lighter fluid is above the interface. The perturbation method is used to obtain solutions to the fifth order for interface profile, velocity potential and oscillati...
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| Veröffentlicht in: | Comptes Rendus Mécanique 2016-03, Vol.344 (3), p.137-150 |
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| container_title | Comptes Rendus Mécanique |
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| creator | Allalou, Nabil Trea, Imane Boughazi, Dalila Debiane, Mohammed Kharif, Christian |
| description | Two-dimensional periodic gravity-capillary waves at the interface between two unbounded fluids with different density are analyzed. The lighter fluid is above the interface. The perturbation method is used to obtain solutions to the fifth order for interface profile, velocity potential and oscillation frequency. The solutions have been carefully controlled by other solutions (third-order surface gravity-capillary solutions, third-order interface gravity waves and fifth-order surface gravity waves). These solutions can be used to describe the qualitative nature of small-amplitude traveling waves and provide initial guesses for numerical solutions to the full Euler system. The results highlight the significant influence on wave profile and wave frequency. In addition, this study extends the Wilton singularity to interfacial waves. |
| doi_str_mv | 10.1016/j.crme.2015.12.001 |
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| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Approximation Computational fluid dynamics Fluid flow Fluid mechanics Fluids Gravity waves Gravity-capillary interfacial wave Harmonic resonance Mathematical analysis Mathematical models Mechanics Perturbation method Perturbation methods Physics |
| title | A fifth-order approximation to gravity-capillary interfacial waves of infinite depth |
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