In order to analyze the stability of gravity–capillary short-crested waves propagating at the interface of two fluids of infinite depths, a numerical procedure has been developed using a collocation method. The three-dimensional wave is generated by an oblique reflection of a uniform wave train arriving at a vertical wall at some angle of incidence measured from the perpendicular to the wall. Fixing the reflection at angle , and wave steepness at , we studied the influence of the density ratio and the inverse Bond number on the unstable area and the growth rate. It was observed that the unstable regions and the maximum growth rate decrease when and increase. Also, we found that the dominant instability belongs to the Class Ib as in the case of free-surface gravity waves in deep water.
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Sara Chikhi 1 ; Mohammed Debiane 1 ; Nabil Allalou 1
@article{CRMECA_2022__350_G1_191_0, author = {Sara Chikhi and Mohammed Debiane and Nabil Allalou}, title = {On the sub-harmonic instabilities of three-dimensional interfacial gravity{\textendash}capillary waves in infinite depths}, journal = {Comptes Rendus. M\'ecanique}, pages = {191--203}, publisher = {Acad\'emie des sciences, Paris}, volume = {350}, year = {2022}, doi = {10.5802/crmeca.111}, language = {en}, }
TY - JOUR AU - Sara Chikhi AU - Mohammed Debiane AU - Nabil Allalou TI - On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths JO - Comptes Rendus. Mécanique PY - 2022 SP - 191 EP - 203 VL - 350 PB - Académie des sciences, Paris DO - 10.5802/crmeca.111 LA - en ID - CRMECA_2022__350_G1_191_0 ER -
%0 Journal Article %A Sara Chikhi %A Mohammed Debiane %A Nabil Allalou %T On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths %J Comptes Rendus. Mécanique %D 2022 %P 191-203 %V 350 %I Académie des sciences, Paris %R 10.5802/crmeca.111 %G en %F CRMECA_2022__350_G1_191_0
Sara Chikhi; Mohammed Debiane; Nabil Allalou. On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths. Comptes Rendus. Mécanique, Volume 350 (2022), pp. 191-203. doi : 10.5802/crmeca.111. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.111/
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