Linear asymptotic phase of the contact surface ripple growth in Richtmyer-Meshkov-like flows

The Richtmyer-Meshkov Instability develops when a planar shock collides with a corrugated interface between two fluids. A shock is transmitted and a shock or rarefaction is reflected back. Due to front waves corrugation, hydrodynamic perturbations are generated in the compressed/expanded fluids which drive the Interface Ripple Growth (IRG) in time. When wave fronts are far away and regain planar shape (in ideal gases), no more pressure perturbations exist inside the bulks.

The linear IRG has two phases: a transient compressible phase in which oscillations due to sound waves are noticed; and, a linear incompressible phase when IRG reaches its asymptotic velocity. For this period, a temporal law of the form: ψ_i (t) =  ψ_∞ + u_i t, where u_i is the growth rate, and ψ_∞ is an asymptotic ordinate to the origin [1,2]. A comparison with experiments and simulations has been done showing a very good agreement between theory and experiments/simulations done in a wide range of regimes for the cases in which the initial ripple amplitude is small enough [1,2].

In this work, a study of the linear IRG is presented. Besides, it is shown that u_i and ψ_∞ are useful quantities for incompressible models in order to take into account compressibility effects occur during the transient phase.