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Simulation numérique des ondes de Faraday

Abstract : When two immiscible fluid layers are subjected to vertical vibration, standing waves appear at the interface if the oscillation amplitude is sufficiently large. Recent work has shown an astonishing variety of patterns, which has contributed to the current interest in the Faraday problem. We have carried out the first complete three-dimensional simulation of Faraday waves. The algorithm we use combines a projection method to solve the Navier-Stokes equations with a Front-Tracking method to treat the interface. The neutral curves and temporal modes agree with Floquet theory. We then simulated the Faraday problem under the conditions in which square and hexagonal patterns appear. The spatio-temporal spectra of the simulated patterns agree with experiment. Nevertheless, the hexagons destabilize in favor of a an alternating sequence of patterns with different symmetries, suggesting the presence of a homoclinic orbit. We have developed an algorithm which forces the hexagonal symmetry in order to calculate the fixed point of this orbit. Finally, we have carried out a numerical study of the drift instability in the Faraday experiment. A horizontal displacement of initially stationary patterns has been experimentally observed when the oscillation amplitude exceeds a secondary threshold. Our numerical simulations have confirmed this result. Bifurcation diagrams displaying additional instabilities have been constructed, as well as a complementary spatio-temporal spectral analysis.
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Submitted on : Tuesday, March 8, 2011 - 11:49:54 AM
Last modification on : Friday, August 5, 2022 - 11:54:10 AM


  • HAL Id : pastel-00574546, version 1


Nicolas Périnet. Simulation numérique des ondes de Faraday. Acoustique [physics.class-ph]. Université Pierre et Marie Curie - Paris VI, 2010. Français. ⟨pastel-00574546⟩



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