Short paper
On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths
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 $\theta$ measured from the perpendicular to the wall. Fixing the reflection at angle $\theta =45\text{°}$, and wave steepness at $h=0.25$, we studied the influence of the density ratio $\mu$ and the inverse Bond number $\delta$ on the unstable area and the growth rate. It was observed that the unstable regions and the maximum growth rate decrease when $\mu$ and $\delta$ 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.

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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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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