On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths
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 arri...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2022-05-01
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| Series: | Comptes Rendus. Mécanique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.111/ |
| _version_ | 1797651471252062208 |
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| author | Chikhi, Sara Debiane, Mohammed Allalou, Nabil |
| author_facet | Chikhi, Sara Debiane, Mohammed Allalou, Nabil |
| author_sort | Chikhi, Sara |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T16:15:09Z |
| format | Article |
| id | doaj.art-5e64bcca05c340aa89b3a23e3a74432a |
| institution | Directory Open Access Journal |
| issn | 1873-7234 |
| language | English |
| last_indexed | 2024-03-11T16:15:09Z |
| publishDate | 2022-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj.art-5e64bcca05c340aa89b3a23e3a74432a2023-10-24T14:21:04ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342022-05-01350G119120310.5802/crmeca.11110.5802/crmeca.111On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depthsChikhi, Sara0https://orcid.org/0000-0001-6799-7341Debiane, Mohammed1Allalou, Nabil2Université des Sciences et de la Technologie Houari Boumediene, Faculté de Physique, BP 32 El Alia, Alger 1611, AlgérieUniversité des Sciences et de la Technologie Houari Boumediene, Faculté de Physique, BP 32 El Alia, Alger 1611, AlgérieUniversité des Sciences et de la Technologie Houari Boumediene, Faculté de Physique, BP 32 El Alia, Alger 1611, AlgérieIn 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.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.111/Short-crested water wavesLinear stabilitySub-harmonic perturbationThree-dimensional wavesGravity–capillary wavesInterfacial wavesShort-crested water waves |
| spellingShingle | Chikhi, Sara Debiane, Mohammed Allalou, Nabil On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths Comptes Rendus. Mécanique Short-crested water waves Linear stability Sub-harmonic perturbation Three-dimensional waves Gravity–capillary waves Interfacial waves Short-crested water waves |
| title | On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths |
| title_full | On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths |
| title_fullStr | On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths |
| title_full_unstemmed | On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths |
| title_short | On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths |
| title_sort | on the sub harmonic instabilities of three dimensional interfacial gravity capillary waves in infinite depths |
| topic | Short-crested water waves Linear stability Sub-harmonic perturbation Three-dimensional waves Gravity–capillary waves Interfacial waves Short-crested water waves |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.111/ |
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