Abstract

Co-authors: Hong Liu (MIT), Allan Adams (MIT)

According to holography, turbulent flows in relativistic boundary conformal field theories should be dual to dynamical black hole solutions in asymptotically AdS_{d+2} spacetime with d the number of spatial dimensions the turbulent flow lives in. This immediately raises many interesting questions about gravitational dynamics. For example, what distinguishes turbulent black holes from non-turbulent ones? What is the gravitational origin of energy cascades and the Kolmogorov scaling observed in turbulent fluid flows?

We construct turbulent black holes in asymptotically AdS_4 spacetime by numerically solving Einstein’s equations. 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. I will argue that statistically steady-state black holes dual to d dimensional turbulent flows have horizons which are approximately fractal with fractal dimension D = d + 4/3. Time permitting I will discuss qualitative differences between holographic superfluid turbulence normal fluid turbulence.