Abstract
We find a quantitative approximation which explains the appearance and amplification of surface waves in a highly viscous fluids when it is submitted to vertical accelerations (Faraday’s instability). Although stationary surface waves with frequency equal to half of the frequency of the excitation are observed in fluids of different kinematical viscosities we show here that the mechanism which produces the instability is very different for a highly viscous fluid as compared with a weakly viscous fluid. This can be shown by-deriving an exact equation for the linear evolution of the surface which is non-local in time. For a highly viscous fluid, this equation becomes local and of second order and is a Mathieu equation which is different from the one found for weak viscosity. Analyzing the new equation, an intimate relation with the Rayleigh-Taylor instability can be found.
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Cerda, E.A. (2000). A parametric oscillator in a highly viscous fluid. In: Tirapegui, E., Martínez, J., Tiemann, R. (eds) Instabilities and Nonequilibrium Structures VI. Nonlinear Phenomena and Complex Systems, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4247-2_7
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DOI: https://doi.org/10.1007/978-94-011-4247-2_7
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