N-Vortex Problems

控制流体力学的欧拉方程的离散模型将进行分析，以了解高雷诺数湍流的目标。全面的方法将涉及一个组合的哈密顿动力系统的数学分析，物理建模的基础上离散粒子表示的欧拉方程，和高性能计算。数学问题是N体类型的，因此这些系统的数值算法开发和动力系统可视化技术将是该奖项下开展的工作的重要组成部分。提案中描述的四个主要项目均旨在开发动力系统理论中的新分析技术，在物理基础良好的模型上测试当前技术，开发粒子相互作用问题的新数值算法和可视化方法，并将模型推向应用。该项目涉及流体流动的离散模型的开发，使用数学工具和高性能计算的组合。一个主要的重点将是研究这些模型的表面上的一个球体，旋转和非旋转，一个问题，它有直接的应用程序在行星大气中的流动在这样的大尺度上，行星的曲率起着作用的动力学。这个问题对于理解地球大气和海洋的环境过程以及木星大气中观察到的大漩涡（包括红斑）可能非常重要。

Discrete models of the Euler equations governing fluid mechanics will be analyzed with the goal of understanding high Reynolds number turbulent flows. The comprehensive approach will involve a combination of mathematical analysis of Hamiltonian dynamical systems, physical modeling based on discrete particle representations of the Euler equations, and high performance computing. The mathematical problem is of N-body type, thus numerical algorithm development for these systems and dynamical systems visualization techniques will be an essential component of the work carried out under this award. The four main projects described in the proposal are each designed to develop new analytical techniques in dynamical systems theory, test current techniques on models that are physically well grounded, develop new numerical algorithms and visualization methods for particle interaction problems, and push the models closer towards applications.This project involves the development of discrete models for fluid flow, using a combination of mathematical tools and high performance computing. One major emphasis will be on studying these models on the surface of a sphere, both rotating and non-rotating, a problem which has direct applications to the flow in a planetary atmosphere on such large scales that the curvature of the planet plays a role in the dynamics. This problem is potentially of great importance to the understanding of environmental processes in the atmospheres and oceans of Earth and to the large vortices, including the Red Spot, observed in the atmosphere of Jupiter.