Evolution equation for bidirectional surface waves in a convecting fluid | Zendy

M. C. Depassier | Zendy

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Evolution equation for bidirectional surface waves in a convecting fluid

Author(s) -

M. C. Depassier

Publication year - 2006

Publication title -

physics of fluids

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.188

H-Index - 180

eISSN - 1089-7666

pISSN - 1070-6631

DOI - 10.1063/1.2362843

Subject(s) - physics , instability , boussinesq approximation (buoyancy) , dissipation , classical mechanics , mechanics , surface wave , work (physics) , convection , optics , thermodynamics , natural convection , rayleigh number

Surface waves in a heated viscous fluid exhibit a long wave oscillatoryinstability. The nonlinear evolution of unidirectional waves is known to bedescribed by a modified Korteweg-deVries-Kuramoto-Sivashinsky equation. In thepresent work we eliminate the restriction of unidirectional waves and find thatthe evolution of the wave is governed by a modified Boussinesq system . Aperturbed Boussinesq equation of the form $y_{tt}-y_{xx} -\epsilon^2(y_{xxtt} +(y^2)_{xx})+ \epsilon^3(y_{xxt}+y_{xxxxt} + (y^2)_{xxt}) =0 $ which includesinstability and dissipation is derived from this system.Comment: 8 pages, no figure

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