Parameterization of Small Scale Flow Structures in Earth's Outer Core

EAR-0000400洛珀，大卫这是一项对与地核和地球发电机问题相关的小尺度流动进行建模、分析和参数化的建议。研究项目将分为三个阶段，大致与赠款的三年期限一致。第一阶段包括显式求解旋转流体中由指定(高斯)形状的小浮体产生的局部速度场和磁场，包括粘性力、洛伦兹力、惯性力和环境层结的影响。项目的这一部分是最直接的，尽管确定上升速度可能需要解决包括惯性或分层在内的非线性问题。在第二阶段，第一阶段得到的解将被推广，以包括流体流动引起的地块变形的影响以及与之相关的流动结构的时间演化。此外，还将从初始静态开始，分析与高斯星团相关的尾迹结构的短期时间发展。预计这一阶段将涉及经典分析和数值计算的结合。在第三阶段，前两个阶段的解将被用来量化(即，参数化)四个重要的非线性效应：螺旋度、电动势、雷诺应力和有效扩散系数。前两种方法对开发更真实的a-w和a2发电机模型很重要，而后两种方法应有助于改进全三维数值模式中的小尺度运动的参数化。

EAR-0000400 Loper, David This is a proposal to model, analyze and parameterize small-scale flows relevant to Earth's core and the geodynamo problem. The research project will consist of three phases, roughly coinciding with the three year duration of the grant. The first phase consists of solving explicitly for the local velocity and magnetic fields generated in a rotating hydromagnetic fluid by a small-scale buoyant parcel of prescribed (Gaussian) shape, including effects of the viscous, Lorentz and inertia forces and ambient stratification. This portion of the project is the most straightforward, although determination of the rise velocity may require solution of a non-linear problem when inertia or stratification is included. In the second phase the solutions obtained during the first phase will be generalized to include the effect of parcel deformation by the fluid flow and the associated temporal evolution of the flow structures. Also, the short-term temporal development of the wake structure associated with a Gaussian parcel, starting from an initial static state, will be analyzed. It is anticipated that this phase will involve a combination of classical analysis and numerical computation. In the third phase the solutions found during the first two phases will be used to quantify (i.e., parameterize) four important nonlinear effects: helicity, electromotive force, Reynolds stress and effective diffusivity. The first two of these are important in the development of more realistic a-w and a2 dynamo models, while the last two should lead to an improvement in the parameterization of small-scale motions in fully 3-D numerical models.