Holographic turbulence, chaotic dynamics and horizon geometry

Abstract: The fluid/gravity correspondence relates black hole dynamics in Anti-de Sitter space to fluid flow in a theory with a conformal equation of state.  Our goal is to translate the long-standing problem of explaining anomalous scaling exponents of fluid velocity structure functions into a language of gravity. To motivate this, we discuss and review how the same duality provided valuable insights into chaotic dynamics by using its dual gravity description. Both for chaos and turbulent flow the expansion rate at the horizon, the surface gravity and the horizon curvature encode information about the dual quantities in question, i.e. the Lyapunov exponents for chaotic dynamics and the anomalous scaling exponents for turbulence. The scaling exponents can be shown to be related to higher moments of the extrinsic curvature of the dual horizon. To test this, we study the fluid phase of conformal matter driven by a randomly fluctuating gravitational potential, numerically solving the evolution of a black hole in Anti-de Sitter space with a fluctuating, stochastic boundary metric.  We observe a scaling behavior of the energy power spectrum that is consistent with compressible flow and compute the energy dissipation and the fluid velocity distribution.