Shocks and Universal Statistics in (1+1)-Dimensional Relativistic Turbulence

TL;DR

This paper investigates the universal statistical properties of relativistic turbulence in (1+1) dimensions, focusing on shock wave contributions, stability, and anomalous exponents, with implications for understanding turbulence and singularities.

Contribution

It analytically studies shock wave effects on structure functions and anomalous exponents in relativistic turbulence, highlighting universality and stability in the (1+1)-dimensional case.

Findings

Shock waves dominate the inertial range structure functions.

Shock stability is demonstrated through analysis.

Anomalous exponents are explicitly calculated.

Abstract

We propose that statistical averages in relativistic turbulence exhibit universal properties. We consider analytically the velocity and temperature differences structure functions in the (1+1)-dimensional relativistic turbulence in which shock waves provide the main contribution to the structure functions in the inertial range. We study shock scattering, demonstrate the stability of the shock waves, and calculate the anomalous exponents. We comment on the possibility of finite time blowup singularities.