Hydrothermal Surface-Wave Instability and the Kuramoto-Sivas

We consider a system formed by an infinite viscous liquid layer with a constant horizontal temperature gradient, and a basic nonlinear bulk velocity profile. In the limit of long-wavelength and large nondimensional surface tension, we show that hydrotherma

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aHYDROTHERMALSURFACE-WAVEINSTABILITYANDTHEKURAMOTO-SIVASHINSKYEQUATIONR.A.Kraenkel,J.G.PereiraInstitutodeF´ sicaTe´oricaUniversidadeEstadualPaulistaRuaPamplona14501405-900S aoPauloSP–BrazilM.A.MannaLaboratoiredePhysiqueMath´ematiqueUniversit´edeMontpellierII34095MontpellierCedex05–FranceAbstractWeconsiderasystemformedbyanin niteviscousliquidlayerwithacon-stanthorizontaltemperaturegradient,andabasicnonlinearbulkvelocitypro le.Inthelimitoflong-wavelengthandlargenondimensionalsurfaceten-sion,weshowthathydrothermalsurface-waveinstabilitiesmaygiveriseto

disturbancesgovernedbytheKuramoto-Sivashinskyequation.Apossible

connectiontohot-wireexperimentsisalsodiscussed.

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