Hydrothermal Surface-Wave Instability and the Kuramoto-Sivas(10)

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

Onlywhenanonlinearreturn owsolutionissupposed,whichisindeedmoreappropriateforaclosedsystem,long-wavehydrothermalphenomenaappear.Therefore,wethinkitwouldbeinterestingtoreexaminetheideasproposedinRef.[16]forthehotwireprobleminthelightofthepresentresults.

Insummary,wehavemadeinthisletteranonlinearanalysisofthelongwavelengthhy-drothermalinstabilities,whichcanbeconsideredasanextensionofaproblem rstdiscussedbySmithandDavis[1]inalinearapproximation.Wehaveshownthatthefree-surfacedy-namicsisgovernedbytheKuramoto-Sivashinskyequation,andthatthepreviousresultscanberecoveredfromoursasaparticularcase.

ACKNOWLEDGMENTS

Twooftheauthors(R.A.K.andJ.G.P.)wouldliketothankConselhoNacionaldeDesenvolvimentoCient´ coeTecnol´ogico(CNPq),Brazil,forpartialsupport.

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