Modeling Interfacial Instabilities With a Modal Model

The well-known Rayleigh-Taylor (RTI) and Richtmyer-Meshkov (RMI) instabilities occur at the interface between two fluids. Though the two problems have been researched extensively, accurate modeling of the growth of an interface into a mixing layer is exceedingly difficult. A pseudospectral modal model was developed to predict early-time, sub-grid, growth of the mixing layer for RTI and RMI; in the multi-physics code xRage. The modal model couples a weakly nonlinear single mode growth model (Goncharov) to a weakly nonlinear multi-mode model (Haan). Both approaches are semi-analytical derivations that are solved to completion through numerical integration. The complete modal model (Goncharov-Haan) evolves the interfacial surface into a mixing layer. By integrating the displacement of the surface along the interface, turbulence closure variables, such as turbulent kinetic energy and length scale, are calculated which are used to dynamically initialize the BHR turbulence model in xRage. As the mixing layer grows, individual modes interact producing new modes that result in a non-locally determined mixing layer. The modal model is demonstrated for a few cases of interest. Results and their implications will be discussed.