Relativistic effects on the Richtmyer-Meshkov instability

TL;DR

This paper investigates how relativistic effects influence the Richtmyer-Meshkov instability, revealing that the growth rate depends on the fluid's equation of state and decreases at high velocities, with implications for high-energy physics and fusion research.

Contribution

It provides the first analysis of relativistic effects on RM instability, showing the dependence on the equation of state and the decrease of growth rate at ultrarelativistic speeds.

Findings

Growth rate depends on the fluid's equation of state.

Growth rate decreases and vanishes at ultrarelativistic speeds.

Numerical simulations characterize non-linear evolution of the instability.

Abstract

Theoretical and numerical analysis of the relativistic effects on the Richtmyer-Meshkov (RM) instability reveals new and potentially very useful effects. We find that, in contrast with the non- relativistic case, the growth rate of the RM instability depends strongly on the equation of state of the fluid, opening up the possibility to infer equations of state from experimental observations of the RM instability. As opposed to the non-relativistic case, we also discover that, above a critical value of the fluid velocity, the growth rate of the instability counter-intuitively decreases due to the Lorentz's factor, and vanishes in the ultrarelativistic limit, as the speed of the particles approaches the speed of light. Both effects might prove very useful for leading-edge applications, such as the study of the equation of state of quark-gluon matter, and the design of fast ignition inertial confinement fusion (ICF) schemes. We perform a linear stability analysis to characterize the instability, for an arbitrary equation of state, and implement numerical simulations to study the instability in the non-linear regime, using the equation of state of an ideal gas. Furthermore, based on the numerical results, we propose a general expression that characterizes the long term evolution of the instability.