Dynamics Of Singularities In Problems Of Fluid Mechanics

9500986 Tanveer研究员建议在流体力学中的一类问题中研究复杂奇点的动力学及其物理含义，这些问题除了界面流动(开尔文-亥姆霍兹，瑞利-泰勒)和通过多孔介质的流动外，还包括三维欧拉方程和纳维-斯托克斯方程。其主要目的是随着粘度或表面张力等规则化参数的逐渐减小，来预测随时间演变的流动的日益复杂的特征。为了达到这一目标，他建议使用分析和数值方法相结合的方法来理解复杂奇点如何、何时和在哪里接近导致小尺度选择性放大的真实物理域。现象素对初始状态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，人们喜欢根据它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，这些参数可以是表面张力、粘度或其他类似的影响。对这种相关性的详细了解可能有助于提取高度复杂流动(如湍流)的有价值的聚集特征。首席研究员建议使用一些相对较新的技术，这些技术在其他问题上证明是有用的。***

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. ***