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Comptes Rendus. Mécanique
Short paper
On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths
Sara Chikhi1 ; Mohammed Debiane1; Nabil Allalou1
1 Université des Sciences et de la Technologie Houari Boumediene, Faculté de Physique, BP 32 El Alia, Alger 1611, Algérie
Comptes Rendus. Mécanique, Volume 350 (2022), pp. 191-203.

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 θ measured from the perpendicular to the wall. Fixing the reflection at angle θ=45°, and wave steepness at h=0.25, we studied the influence of the density ratio μ and the inverse Bond number δ on the unstable area and the growth rate. It was observed that the unstable regions and the maximum growth rate decrease when μ and δ 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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Revised:
Accepted:
Published online:
DOI: 10.5802/crmeca.111
Keywords: Linear stability, Sub-harmonic perturbation, Three-dimensional waves, Gravity–capillary waves, Interfacial waves, Short-crested water waves
Sara Chikhi 1; Mohammed Debiane 1; Nabil Allalou 1

1 Université des Sciences et de la Technologie Houari Boumediene, Faculté de Physique, BP 32 El Alia, Alger 1611, Algérie 
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     title = {On the sub-harmonic instabilities of three-dimensional interfacial gravity{\textendash}capillary waves in infinite depths},
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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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