Turbulence and Perturbed Black Holes

We study the dynamics of a 2+1 dimensional relativistic viscous conformal fluid, extending previous analysis of solutions in the perfect fluid case (Carrasco et al, 2012) on a flat background. Such fluid solutions arise as duals, under the "fluid/gravity duality", to 3+1 dimensional asymptotically anti-de Sitter (AAdS) black brane solutions to Einstein's equation.  We examine stability properties of shear flows, which correspond to certain quasinormal modes of the black brane.  We find that, for sufficiently high Reynolds number, the solution undergoes an inverse turbulent cascade to long wavelengths, until two counter-rotating slowly decaying vortices remain. Our results suggest a new and interesting feature of the behavior of perturbed AAdS black holes and black branes, which is not captured by a standard quasinormal mode analysis.  Namely, for sufficiently large black objects (with long-lived quasinormal modes), nonlinearities transfer energy from short to long wavelength modes with a consequent impact on the decaying properties of the solution.  These results are in accord with very recent bulk general relativity simulations of Adams et al (2013).