Studies of 3D Convection with Temperature-Dependent Viscosity

为了更好地理解地幔对流的物理性质，PI将研究具有强烈温度依赖性粘度v(T)的流体中的三维热对流。这项工作的一个重要动机是更好地理解地球板块构造速度场的环面分量是如何产生的。本工作包括三个部分：(A)用数值（伽辽金方法）研究了具有v(T)无应力边界的无限普朗特数流体中的稳定方胞对流，并详细研究了结果解的稳定性。(B)采用具有多种流变规律和加热模式的单模态和多模态平均场方程，研究了三维高瑞利数对流中多面体-环面耦合。(C)自由表面v(T)流体对流的实验研究，以测量作为瑞利数和粘度对比函数的多面体-环面耦合程度。

In order to better understand the physics of convection in the Earth's mantle, the PI will study three-dimensional thermal convection in a fluid with a strongly temperature dependent viscosity v(T). An important motivation of the work is to better understand how the toroidal component of the Earth's plate tectonic velocity field is generated. The work comprises three parts: (A) A numerical (Galerkin method) investigation of steady square cell convection in an infinite Prandtl number fluid with v(T) stress-free boundaries, together with a detailed study of the stability of the resulting solutions. (B) A study of poloidal-toroidal coupling in 3D high Rayleigh number convection, using the single- and multi-mode mean field equations with a variety of rheological laws and heating modes. (C) An experimental study of convection in a v(T) fluid with a free surface, to measure the degree of poloidal-toroidal coupling as a function of Rayleigh number and viscosity contrast.