Analytical Solutions of Layzer-Type Approach to Unstable Interfacial Fluid Mixing

We extend the Layzer-type approach to unstable interfacial fluid mixing, applied up to now only to vacuum bubbles, to spikes and derive the analytical solutions of the model for the positions, velocities, accelerations, and curvatures at the tips of the bubble and spike over all times. The analytical predictions are in good agreement with the results from numerical simulations for both spikes and bubbles. We give the first analytical prediction for the asymptotic growth rate of a spike at the Richtmyer-Meshkov unstable interface. We predict that, in contrast to the asymptotic bubble growth rate, the asymptotic growth rate of a spike at the Richtmyer-Meshkov unstable interface is a constant and depends on the initial condition.