Rayleigh-Bénard Convection and Faraday Instability in Quasi-Periodic Regimes: Theory and Experiment

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In this project, we propose to investigate the Faraday instability in the case when the vertical acceleration is quasi-periodic with two incommensurate frequencies. In this situation the Floquet theory cannot be used to determine a stability criterion. Therefore, new strategy based on harmonic balance and Lyaponouv exponent will be required to investigate the linear onset of instability in quasi-periodic regimes. We will focus our attention to a non-viscous fluid, weakly viscous fluid and highly viscous fluid. The linear study of instability will be accompanied with a weakly non-linear analysis and experiments.In a second part we study the effect of gravitational modulation on the onset of convection when the oscillations of the fluid layer are periodic or quasi-periodic. Here we expect also an instability in a zero gravity environment, which is of interest for experiments in a space lab. The case where the fluid is heated from above will be also studied. Beneath experiments, a weakly non-linear analysis as well as a fully numerical treatment of the basic equations will be done.