Scaling Relations in Two-Dimensional Relativistic Hydrodynamic Turbulence

TL;DR

This paper derives exact scaling relations for 2D relativistic hydrodynamic turbulence, supported by simulations, and explores implications for gravitational fields via fluid-gravity correspondence.

Contribution

It introduces novel exact scaling relations for 2D relativistic turbulence and links these to gravitational phenomena through the fluid-gravity correspondence.

Findings

Derived exact scaling relations for energy and enstrophy cascades.

Numerical simulations validate the theoretical relations.

Implications for gravitational fields in AdS spacetimes are discussed.

Abstract

We derive exact scaling relations for two-dimensional relativistic hydrodynamic turbulence in the inertial range of scales. We consider both the energy cascade towards large scales and the enstrophy cascade towards small scales. We illustrate these relations by numerical simulations of turbulent weakly compressible flows. Intriguingly, the fluid-gravity correspondence implies that the gravitational field in spacetimes with anti-de Sitter asymptotics should exhibit similar scaling relations.