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. ***
