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Résumé |
The fluid/gravity correspondence, the duality between black hole dynamics in Anti-de Sitter space and hydrodynamics, may be used to geometrize turbulent flow. Our goal is to translate the long-standing problem of explaining anomalous scaling exponents of fluid velocity structure functions into a language of gravity. 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. Subtleties regarding the fluid's compressibility in this set up are discussed. 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. We identify observables in the dual gravity theory corresponding to higher moments of the averaged energy dissipation which help to map anomalous scaling exponents to covariant quantities defined on the dual horizon. |
