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

9220061 Parmentier本研究将在数值实验的基础上探索无限普朗特数流体中高瑞利数三维热对流的物理过程。到目前为止，对从上面冷却的体积加热流体的数值实验表明，在顶部边界热边界层以下的流体基本上是非绝热的，这与通常关于高Ra时热对流结构的假设相反。流动的结构由冷边界层提供的近轴对称的羽状物组成。线形构造可能代表了对流地幔中的俯冲带，但很少出现。PI将进行进一步的数值实验，包括从下加热以及体积加热。主要的创新是一种用于浮力粘性流动的多重网格迭代求解器，其速度比经常用于三维对流问题的FFT方法快一个数量级或更快。PI将把多重网格解算器的发展扩展到具有可变粘性的浮力裂隙流。这将通过求解以原始变量(压力和速度分量)而不是向量流函数和涡度或一些其他势函数公式表示的方程来实现。这一新方法的第一个应用将是了解温度和深度依赖的粘度如何修改恒粘度、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. ***