Construction and validation of a statistical model for the nonlinear Kelvin-Helmholtz instability under compressible, multimode conditions

Abstract

A new model for the evolution of compressible, multimode Kelvin-Helmholtz (KH) instability is presented. The model is built upon compressible single vortex evolution and two-vortex interaction, resulting in a statistical description of the compressible KH mixing zone evolution. These two building blocks, which, due to complicated compressibility effects and the presence of shock waves, cannot be derived using simple flow models, are validated by novel supersonic high-energy-density physics experiments. The model was validated against numerical simulations, experimental results, and previous phenomenological models, confirming the compressible KH scaling law in the self-similar regime in good agreement with simulations and a compilation of experimental data. Moreover, the model extends and confirms the logical validity of previous work, done in the incompressible regime. Therefore, it sheds new light on the evolution of compressible shear layers up to the self-similar regime.