Український математичний конгрес - 2009
Qiang Zhang (City University of Hong Kong, Kowloon, Hong Kong)
Nonlinear Theories for Shock-induced Interfacial Instabilities
It is well known that, when a shock propagates through a material interface that separates fluids of different densities, the interface becomes unstable and fingers develop. It is a long-standing problem to develop a theory to predict the size of these fingers. In this talk, we present an analytical nonlinear theory that provides predictions for the growth rate and the size of the fingers in fluids. The theoretical predictions are in remarkably good agreement with the results from full-scale numerical simulations. We also study this fingering instability in granular systems. We show that if the collisions between the particles conserve energy, the behavior of generalized fingering instability in granular materials is very similar to that of classical instability in fluids. However, our study also showed a very surprising result: the energy loss during particle collisions, even when it is very small, causes growth of the fingers in granular systems to be dramatically different from that in fluids. The fingers formed by the light particles grow faster and become longer and narrower than the fingers formed by the heavy particles. This is completely opposite to the well-known behavior of fingers in fluids, In addition, the finger composed of light particles collapse into an extremely compact, tortuous filament, and diffusive mixing between particle types at the particle scale is heavily suppressed.