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

准周期状态下的瑞利-贝纳德对流和法拉第不稳定性：理论与实验

• 批准号: 5276144
• 负责人: Professor Dr. Michael Bestehorn
• 金额: --
• 依托单位: Maariftory of Mechanics University Hassan II Ain Chok (aufgelöst)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2000
• 资助国家: 德国
• 起止时间: 1999-12-31 至 2004-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5276144?language=en
• 关键词: Rayleigh; nard; Convection; Faraday; Instability

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.

在这个项目中，我们建议在垂直加速度为准周期且具有两个无公度频率的情况下研究法拉第不稳定性。在这种情况下，弗洛奎理论不能用来确定稳定性判据。因此，需要一种新的基于调和平衡和Lyaponouv指数的方法来研究准周期系统的线性不稳定性。我们将重点关注无粘性流体、弱粘性流体和高粘性流体。对不稳定性的线性研究将伴随着弱非线性的分析和实验。在第二部分中，我们研究了当流体层的振荡是周期或准周期时，重力调制对对流开始的影响。在这里，我们预计在零重力环境中也会出现不稳定性，这对于空间实验室的实验来说是很有意义的。流体从上方加热的情况也将被研究。在实验下，将对基本方程进行弱非线性分析和完全数值处理。