Evolution equation for bidirectional surface waves in a convecting fluid

M. C. Depassier

doi:10.1063/1.2362843

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arXiv · nlin/0603023

Evolution equation for bidirectional surface waves in a convecting fluid

M. C. Depassier

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Abstract

Surface waves in a heated viscous fluid exhibit a long wave oscillatory instability. The nonlinear evolution of unidirectional waves is known to be described by a modified Korteweg-deVries-Kuramoto-Sivashinsky equation. In the present work we eliminate the restriction of unidirectional waves and find that the evolution of the wave is governed by a modified Boussinesq system . A perturbed Boussinesq equation of the form $y_{tt}-y_{xx} -ε^2(y_{xxtt} + (y^2)_{xx})+ ε^3(y_{xxt}+y_{xxxxt} + (y^2)_{xxt}) =0 $ which includes instability and dissipation is derived from this system.

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M. C. Depassier. 2006-03-10. Evolution equation for bidirectional surface waves in a convecting fluid. https://doi.org/10.1063/1.2362843

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