AMC-SS: 3D Stochastic Equations of Fluid Dynamics and Wiener Chaos

被称为欧拉和Navier-Stokes方程的偏微分方程是流体和气体运动的最重要的确定性模型。长期以来，人们一直怀疑Navier-Stokes方程或Euler方程的随机版本可能是湍流运动的有价值的模型。要进行的研究是关注发展方法，以指定与湍流有关的流体动力学方程的随机版本，调查其性质，并构建数值近似和渐近。湍流在许多对科学和技术有重要意义的背景下是突出的，包括海洋学，气候学，飞行动力学，导航，燃烧和推进，所提出的研究涉及湍流的基本模型，捕捉其基本行为，并产生计算上易于处理的表示。相关的数值算法将被开发、编码和测试。

The PDEs known as the Euler and Navier-Stokes equations are the most importantdeterministic models for the motion of fluids and gases. It has long beensuspected that stochastic versions of Navier-Stokes or Euler equations couldbe valuable models for turbulent motion. The research to be performed isconcerned with developing methods for specifying stochastic versions ofequations of fluid dynamics related to turbulence, investigating theirproperties, and constructing numerical approximations and asymptotics.Turbulence is prominent in numerous contexts of significance for science andtechnology, including oceanography, climatology, flight dynamics, navigation,combustion and propulsion, etc. The proposed research deals with mathematicalmodels of turbulence that capture its essential behavior, and also yieldcomputationally tractable representations. Related numerical algorithms willbe developed, coded, and tested.