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Asymptotic Description of a Viscous Fluid Layer


We prove that the exact non local equation derived by the present authors for the temporal linear evolution of the surface of a viscous incompressible fluid reduces asymptotically for high viscosity to a second order Mathieu type equation proposed recently by Cerda and Tirapegui. The equation describes a strongly damped pendulum and the conditions of validity of the asymptotic regime are given in terms of the relevant physical parameters.

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Cerda, E., Rojas, R. & Tirapegui, E. Asymptotic Description of a Viscous Fluid Layer. Journal of Statistical Physics 101, 553–565 (2000).

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  • faraday instability
  • viscous fluid