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

小行星9220061 研究将探讨高瑞利数的物理，三维热对流在无限普朗特数流体的数值实验的基础上。 迄今为止完成的数值实验的体积加热的流体从上面冷却表明，在顶部边界处的热边界层以下的流体基本上是非绝热的，与通常的假设相反，在高Ra的热对流的结构。 流动的结构包括由冷边界层供给的近轴对称羽流。 可能代表对流地幔中俯冲带的线性结构很少出现。 PI将进行进一步的数值实验，包括从下面加热以及体积 暖气 主要的创新是一个多重网格迭代求解浮力粘性流，是一个数量级或更快的速度比FFT方法，经常被用于三维对流问题。 PI将扩展多重网格求解器的发展，以浮动粘性粘性流动。 这将通过求解用原始变量（压力和速度分量）而不是矢量流函数和涡量或其他势函数公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性粘度如何修改恒定粘度，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. ***