Abstract: The fluid/gravity correspondence, the duality between the dynamics of black holes in Anti-de Sitter space and the fluid phase of field theories, may be used to geometrize turbulent flow and translate a long standing problem of classical fluid dynamics into a language of gravity. We study the fluid phase of conformal matter driven by a randomly fluctuating gravitational potential, by 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 which correspond to correlators of the fluid velocity and their higher moments which help to map anomalous scaling exponents to covariant quantities defined on the dual horizon.