Dynamics Of Singularities In Problems Of Fluid Mechanics

9500986 Tanveer研究者提出研究复杂奇点的动力学及其在一类问题中的物理含义 在流体力学中，除了界面流动（Kelvin-Helmholtz，Rayleigh-Taylor）和通过多孔介质的流动之外，还包括3-D Euler和Navier-Stokes方程。其主要目标是预测随着时间的推移，随着一些正则化参数，如粘度或表面张力逐渐变小，越来越复杂的功能。为了达到这一目标，他建议采用分析和数值方法相结合，以了解复杂的奇点如何，何时以及在何处接近真实的物理域，导致选择性放大小尺度。 现象对我们初始状态的微小变化的敏感性是物理世界中许多非线性问题的一个众所周知的特征。 在许多情况下，人们喜欢根据其与某些物理参数的关系来量化这种敏感性，在他们的问题中，这些物理参数可以是表面张力、粘度或其他此类效应。详细了解这种依赖关系可能有助于提取有价值的聚合物功能的高度复杂的流动，如湍流。主要研究者建议使用一些相对较新的技术，这些技术在其他问题中已被证明是有用的。 ***

9500986 Tanveer The investigator proposes to investigate the dynamics of complex singularities and their physical implications in a class of problems n fluid mechanics that include the 3-D Euler and Navier-Stokes equations in addition to interfacial flows (Kelvin-Helmholtz, Rayleigh-Taylor) and flow through porous medium. The main goal is to predict increasingly complicated features of a time evolving flow, as some regularizing parameter such as viscosity or surface tension is made progressively small. To reach this goal, he proposes to employ a combination of analytical and numerical methods to understand how, when and where complex singularities approach the real physical domain that leads to selective amplification of small scales. %%% Sensitivity of a phenonemon to small changes in our initial state is a well known feature of many nonlinear problems in the physical world. In many cases, one likes to quantify this sensitivity in terms of its relation to some physical parameter, which in their problems can be either surface tension, viscosity or other such effects. A detailed understanding of this dependence may help in extract valuable aggregate features of of a highly complicated flow such as turbulence. The principal investigator proposes to use some relatively new techniques that have proved useful in other problems. ***