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

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.

arXiv comment37 pages, 7 figures

References in corpus (5)

• Turbulence without pressure
• Universal hydrodynamics of non-conformal branes
• New relations for correlation functions in Navier-Stokes turbulence
• Exact Scaling Relations In Relativistic Hydrodynamic Turbulence
• Statistical Theory for the Stochastic Burgers Equation in the Inviscid Limit

Cited by in corpus (6)

• Turbulent flows for relativistic conformal fluids in 2+1 dimensions
• The holographic dual of a Riemann problem in a large number of dimensions
• Cascades and Dissipative Anomalies in Relativistic Fluid Turbulence
• The Penrose Inequality and the Fluid/Gravity Correspondence
• Scaling Relations in Two-Dimensional Relativistic Hydrodynamic Turbulence
• Steady asymptotic equilibria in conformal relativistic fluids