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

在这个项目中，我们建议研究垂直加速度是两个不相称频率的准周期情况下的法拉第不稳定性。在这种情况下，Floquet理论不能用来确定稳定性判据。因此，需要基于调和平衡和Lyaponouv指数的新策略来研究准周期状态下不稳定性的线性起始。我们将把注意力集中在非粘性流体，弱粘性流体和高粘性流体上。不稳定性的线性研究将伴随着弱非线性分析和实验。在第二部分中，我们研究了当流体层振荡为周期或准周期时，重力调制对对流开始的影响。在这里，我们还期望零重力环境中的不稳定性，这对空间实验室的实验很感兴趣。还将研究从上方加热流体的情况。在实验下，将进行弱非线性分析以及基本方程的完全数值处理。

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.