3D Thermal Convection in an Infinite Prandtl Number Fluid with Application to Mantle Dynamics

[220061] Parmentier本研究将在数值实验的基础上探讨无限普朗特数流体中高瑞利数三维热对流的物理特性。迄今为止完成的从上方冷却的体积加热流体的数值实验表明，在顶部边界的热边界层以下的流体基本上是非绝热的，这与高Ra时热对流结构的通常假设相反。气流的结构由近轴对称的羽流组成，这些羽流由冷边界层供给。线性结构，可能代表了对流地幔中的俯冲带，只是很少出现。PI将进行进一步的数值实验，包括从下面加热和体积加热。主要的创新是浮力粘性流动的多网格迭代求解器，它比3D对流问题中经常使用的FFT方法快一个数量级或更快。PI将扩展多网格求解器的发展到可变粘度的浮力粘性流动。这将通过求解以原始变量（压力和速度分量）而不是矢量流函数和涡量或其他势函数形式表示的方程来实现。这种新方法的第一个应用将是了解温度和深度依赖粘度如何改变恒定粘度，高瑞利数数值实验的结果。＊＊＊

9220061 Parmentier The studies will explore the physics of high Rayleigh number, 3D thermal convection in an infinite Prandtl number fluid based on numerical experiments. Numerical experiments completed thus far for a volumetrically heated fluid cooled from above show that fluid below the thermal boundary layer at the top boundary is substantially non-adiabatic, contrary to the usual assumptions about the structure of thermal convection at high Ra. The structure of the flow consists of nearly axisymmetric plumes that are fed by the cold boundary layer. Linear structures, that would presumably represent subduction zones in the convecting mantle, appear only infrequently. The PI will carry out further numerical experiments that include heating from below as well as volumetric heating. The principal innovation is a multigrid iterative solver for buoyant viscous flow that is an order of magnitude or more faster than the FFT methods that have frequently been used in 3D convection problems. The PI will extend development of multigrid solvers to buoyant fiscous flow with variable viscosity. This will be carried out by solving equations formulated in primitive variable (pressures and velocity components) rather than in vector streamfunction and vorticity or some other potential function formulation. The first application of this new methodology will be to understand how temperature and depth dependent viscosity modify results of the constant viscosity, high Rayleigh number numerical experiments. ***