Studying Universality in the Dynamics of Shock-induced Interfacial Instability

Description

Interfacial fluid mixing is a common phenomenon that occurs frequently in basic scienceresearch and in engineering applications. Very often, the involved interface is unstableand small disturbances at the interface grow and form nonlinear structures, such asfingers and chaotic mixing layers. It is important to understand the growth of suchnonlinear structures. However, many physical parameters can affect the dynamics ofthese nonlinear structures. One needs to perform large numbers of simulations orexperiments to explore the effects of any physical parameter, which can be very timeconsumingand financially expensive. Therefore, it is extremely desirable and importantto study the universal behavior in the dynamics of these nonlinear structures. Theproperty of universality allows us to determine the dominant behavior for a whole classof unstable interfacial mixing problems from a single numerical simulation or a singleexperiment. However, due to the complicated dynamics and nonlinear nature of thephenomena, even performing numerical simulations and experiments for a givenparameter set represents a significant challenge. Therefore, to a large extent, theuniversal behavior in unstable interfacial mixing has not been examined.In this proposal, we will study universality in the behavior of nonlinear structures atunstable interfaces. We will focus on a well-known class of unstable interfacial mixingproblems: the nonlinear structures in a shock-driven interfacial instability. Thisunstable system is challenging to study due to several complications, including fluidcompressibility and the presence of shock and rarefaction waves. For this reason, theissue of universality in the dynamics of a shock-driven interfacial instability has notbeen analyzed. We will conduct such a study in this project.