Holographic Turbulence

We construct turbulent black holes in asymptotically AdS[subscript 4] spacetime by numerically solving Einstein’s equations. Using the AdS/CFT correspondence we find that both the dual holographic fluid and bulk geometry display signatures of an inverse cascade with the bulk geometry being well approximated by the fluid-gravity gradient expansion. We argue that statistically steady-state black holes dual to d dimensional turbulent flows have horizons whose area growth has a fractal-like structure with fractal dimension D=d+4/3.United States. Dept. of Energy (cooperative research Agreement No. DE-FC02- 94ER40818)Massachusetts Institute of Technology (Pappalardo Fellowship in Physics)Simons Foundation (Fellowship)United States. Dept. of Energy (cooperative research Agreement No. DE-FG0205ER41360