Mathematical Sciences: Theoretical and Computational Aspectsof Turbulence

这个项目继续了以前对湍流的研究，结合了数学分析、数值模拟和动力系统的方法。湍流产生于Navier-Stokes方程的解。湍流的永久流型与流动相空间中的吸引子有关。吸引子又可以用近似的惯性流形来逼近。因此，发展与近似惯性流形相对应的数值算法是这项工作的中心主题。湍流是流体流动中的一种基本现象。在描述飞机、船只、泵和发动机的行为时，会出现这样的流。更好地了解湍流将有助于改进这些机器的设计。

This project continues the studies of turbulence undertaken previously, combining mathematical analysis, numerical simulations, and methods from dynamical systems. The turbulent flows arise as solutions of the Navier-Stokes equations. The permanent regime for a turbulent flow is related to an attractor in the phase space of the flow. The attractor in turn is approximable by an approximate inertial manifold. Hence development of numerical algorithms that correspond to approximate inertial manifolds is a central theme of the work. Turbulence is a fundamental phenomenon in fluid flows. Such flows arise in describing the behavior of planes, boats, pumps, and engines. A better understanding of turbulence will help to improve the design of these machines.