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The Kelvin-Helmholtz instabilities in two-fluids shallow water models

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLANNES, David
hal.structure.identifierSchool of Mathematics and Computational Science
dc.contributor.authorMING, Mei
dc.date.accessioned2024-04-04T03:19:43Z
dc.date.available2024-04-04T03:19:43Z
dc.date.issued2015
dc.identifier.issn1069-5265
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194532
dc.description.abstractEnThe goal of this paper is to describe the formation of Kelvin-Helmholtz instabilities at the interface of two fluids of different densities and the ability of vari-ous shallow water models to reproduce correctly the formation of these instabilities. Working first in the so called rigid lid case, we derive by a simple linear anal-ysis an explicit condition for the stability of the low frequency modes of the inter-face perturbation, an expression for the critical wave number above which Kelvin-Helmholtz instabilities appear, and a condition for the stability of all modes when surface tension is present. Similar conditions are derived for several shallow water asymptotic models and compared with the values obtained for the full Euler equa-tions. Noting the inability of these models to reproduce correctly the scenario of formation of Kelvin-Helmholtz instabilities, we derive new models that provide a perfect matching. A comparisons with experimental data is also provided. Moreover, we briefly discuss the more complex case where the rigid lid is re-placed by a free surface. In this configuration, it appears that some frequency modes are stable when the velocity jump at the interface is large enough; we explain why such stable modes do not appear in the rigid lid case.
dc.description.sponsorshipDYnamique des Fluides, Couches Limites, Tourbillons et Interfaces - ANR-13-BS01-0003
dc.description.sponsorshipFrontières, numérique, dispersion. - ANR-13-BS01-0009
dc.language.isoen
dc.publisherSpringer
dc.title.enThe Kelvin-Helmholtz instabilities in two-fluids shallow water models
dc.typeArticle de revue
dc.subject.halPlanète et Univers [physics]/Océan, Atmosphère
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalFields Institute Communications
bordeaux.page185-234
bordeaux.volume75
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01101993
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01101993v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Fields%20Institute%20Communications&rft.date=2015&rft.volume=75&rft.spage=185-234&rft.epage=185-234&rft.eissn=1069-5265&rft.issn=1069-5265&rft.au=LANNES,%20David&MING,%20Mei&rft.genre=article


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