An ejecta model created from combining nonlinear growth and empirical asymptotic spike velocity models

Ejecta models can be formulated from Richtmyer-Meshkov instability behavior where initial ejecta properties are based on wave amplitude, wave number, and spike velocity. While many models employ nonlinear factors, most models are based on incompressible theory and do not account for compressible effects when the incident shock Mach number becomes large. Karkhanis et al. [V. Karkhanis et al., J. Appl. Phys., 2018] developed an empirical model for the asymptotic spike velocity that includes compressibility. The distance particles travel can be overestimated by using the asymptotic speed for initial ejecta formation. For a more accurate trajectory, the ejecta particles can be initialized with an initial spike velocity and then integrated with a nonlinear growth model until the particles reach the asymptotic spike velocity. In this work, the Karkhanis model is combined with the nonlinear growth model in Buttler et al. [W. T. Buttler et al., J. Fluid Mech, 703, 2012, pp. 60-84] to obtain a time varying solution where the asymptotic velocity is recovered in the late time limit.