混合流体Rayleigh-Bénard对流中流动状态多重稳定的数值研究

非线性耗散系统中自组织时空结构形成及其稳定性的研究是非线性科学的前沿课题，混合流体Rayleigh-Bénard（RB）对流是一个研究非线性耗散系统中流动稳定性、分岔、斑图形成和复杂时空行为的模型系统。本项目拟采用高精度数值方法对封闭腔体内混合流体RB对流进行直接数值模拟，研究对流启动点附近行波对流的多重稳定性现象，以及远离启动点的高Rayleigh数下SOC（Stationary Overturning Convection）状态和局部SOC状态的多重稳定性现象与分岔特性；揭示对流结构的形成与稳定机理及腔体侧壁的影响作用；探讨Rayleigh数、Prandtl数、Lewis数、反映Soret效应的分离比和腔体的长高比对对流不稳定和流动结构的影响。本研究将有利于深入理解湍流的形成机理和深刻揭示混合流体对流系统的动力学特性，有助于预测或控制工业生产中混合流体的对流过程。

It is an advanced topic in nonlinear science to research self-organization pattern formation and stability of many nonlinear dissipative systems. Rayleigh-Bénard convection in binary fluid mixtures such as ethanol water, of which complex time-dependence dynamic states present very close to the onset of convection, is a paradigmatic system for studying problems related to stabilities, bifurcations, pattern formation, and complex spatiotemporal behavior of the nonlinear dissipative systems. In this project, using a high-order accuracy numerical method to solve the full hydrodynamic field equations of Rayleigh-Bénard convection system, we will study the multistability phenomena of travelling wave convection around the convection onset, and the multistability phenomena and bifurcations of stationary overturning convection (SOC) and localized SOC for higher Rayleigh numbers far away from the onset. The formation and stability mechanism of convection structure and the effect of lateral boundary walls will be investigated. The dependence of convection structure and instabilities on the Rayleigh number, Prandtl number, Lewis number, separation ratio, and aspect ratio will also be discussed. The study on this project will be beneficial for further revealing the pattern formation and dynamic characteristics of binary mixtures convection, and also helpful for effectively predicting and controlling the convective process of fluid mixtures in industry productions and engineering applications, in which non-equilibrium phenomena are involved.