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.
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Nabil Allalou 1, 2 ; Imane Trea 2 ; Dalila Boughazi 2 ; Mohammed Debiane 2 ; Christian Kharif 3
@article{CRMECA_2016__344_3_137_0, author = {Nabil Allalou and Imane Trea and Dalila Boughazi and Mohammed Debiane and Christian Kharif}, title = {A fifth-order approximation to gravity-capillary interfacial waves of infinite depth}, journal = {Comptes Rendus. M\'ecanique}, pages = {137--150}, publisher = {Elsevier}, volume = {344}, number = {3}, year = {2016}, doi = {10.1016/j.crme.2015.12.001}, language = {en}, }
TY - JOUR AU - Nabil Allalou AU - Imane Trea AU - Dalila Boughazi AU - Mohammed Debiane AU - Christian Kharif TI - A fifth-order approximation to gravity-capillary interfacial waves of infinite depth JO - Comptes Rendus. Mécanique PY - 2016 SP - 137 EP - 150 VL - 344 IS - 3 PB - Elsevier DO - 10.1016/j.crme.2015.12.001 LA - en ID - CRMECA_2016__344_3_137_0 ER -
%0 Journal Article %A Nabil Allalou %A Imane Trea %A Dalila Boughazi %A Mohammed Debiane %A Christian Kharif %T A fifth-order approximation to gravity-capillary interfacial waves of infinite depth %J Comptes Rendus. Mécanique %D 2016 %P 137-150 %V 344 %N 3 %I Elsevier %R 10.1016/j.crme.2015.12.001 %G en %F CRMECA_2016__344_3_137_0
Nabil Allalou; Imane Trea; Dalila Boughazi; Mohammed Debiane; Christian Kharif. A fifth-order approximation to gravity-capillary interfacial waves of infinite depth. Comptes Rendus. Mécanique, Volume 344 (2016) no. 3, pp. 137-150. doi : 10.1016/j.crme.2015.12.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.12.001/
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