Evolution of perturbed accelerating relativistic shock waves

TL;DR

This paper investigates how relativistic shock waves evolve when encountering upstream irregularities, using numerical simulations and analytical methods to understand the stability and effects of turbulence on shock surfaces.

Contribution

It combines numerical simulations with analytical analysis to study the nonlinear evolution of shock surface perturbations in relativistic flows, demonstrating the transient nature of wrinkles caused by upstream turbulence.

Findings

No permanent wrinkles form on the shock surface due to upstream turbulence.

The PLUTO code reliably reproduces known linear perturbation results.

Analytical description of geometrical effects of turbulence on shock surfaces.

Abstract

We study the evolution of an accelerating hyperrelativistic shock under the presence of upstream inhomogeneities wrinkling the discontinuity surface. The investigation is conducted by means of numerical simulations using the PLUTO code for astrophysical fluid dynamics. The reliability and robustness of the code are demonstrated against well known results coming from the linear perturbation theory. We then follow the nonlinear evolution of two classes of perturbing upstream atmospheres and conclude that no lasting wrinkle can be preserved indefinitely by the flow. Finally we derive analytically a description of the geometrical effects of a turbulent upstream ambient on the discontinuity surface.