“ The Impulse Approximation for the Richtmyer - Meshkov Instability in Continuously Stratified Fluids ”

The popular impulse approximation is applied to the Richtmyer-Meshkov problem for continuously strati ed uids through the use of a model due to Sa man and Meiron. The predictions of the late time growth rate of the interface and interfacial circulation from a numerical implementation of the model are compared with calculations from the nonlinear Euler equations. It is shown that for weak incident shocks the impulse approximation, known to be accurate for interfaces of in nitesimal amplitude and thickness, is also very accurate for problems with interfaces of nite amplitude and thickness. For stronger shocks, post-shock values of Atwood ratio, amplitude and layer thickness are used in the model to obtain accurate predictions of late time growth rate for high Atwood ratio con gurations. Poor agreement is seen for low Atwood ratios. Examinations of vorticity distributions reveal that the impulse model does not predict the correct distribution for either high or low Atwood ratios. The Biot-Savart law and direct measurements of the discrete divergence in the ow are used to show that compressible e ects are only important in the initialization of the instability and that the subsequent evolution is determined from the vorticity distribution. The vorticity gener-