On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths

Sara Chikhi; Mohammed Debiane; Nabil Allalou

doi:10.5802/crmeca.111

Short paper

On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths

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

Comptes Rendus. Mécanique, Volume 350 (2022), pp. 191-203.

Abstract

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.

Received: 2021-10-10
Revised: 2022-04-19
Accepted: 2022-04-21
Published online: 2022-05-12

DOI: 10.5802/crmeca.111

Keywords: Linear stability, Sub-harmonic perturbation, Three-dimensional waves, Gravity–capillary waves, Interfacial waves, Short-crested water waves

Author's affiliations:

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

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     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},
}

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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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