Evolution equation for bidirectional surface waves in a convecting fluid
Depassier, M. C.
Original · EN
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 ytt-yxx -ε²(yxxtt + (y²)xx)+ ε³(yxxt+yxxxxt + (y²)xxt) =0 which includes instability and dissipation is derived from this system.
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