Holographic Turbulence From a Random Gravitational Potential

Abstract

We study the turbulent dynamics of a relativistic (2 + 1)-dimensional fluid placed in a stochastic gravitational potential. We demonstrate that the dynamics of the fluid can be obtained using a dual holographic description realized by an asymptotically Anti-de Sitter black brane driven by a random boundary metric. Using the holographic duality we study the inverse cascade energy power spectrum of the fluid and show that it is compatible with that of a compressible fluid flow. We calculate the local energy dissipation and the local fluid velocity distribution which provide other measures of the holographic fluid turbulence.