Forced Fluid Dynamics from Gravity in Arbitrary Dimensions

Abstract: We consider long wavelength solutions to the Einstein-dilaton system with negative cosmological constant which are dual, under the AdS/CFT correspondence, to solutions of the conformal relativistic Navier-Stokes equations with a dilaton-dependent forcing term. Certain forced fluid flows are known to exhibit turbulence; holographic duals of forced fluid dynamics are therefore of particular interest as they may aid efforts towards an explicit model of holographic steady state turbulence. In recent work, Bhattacharyya et al have constructed long wavelength asymptotically locally AdS_5 bulk spacetimes with a slowly varying boundary dilaton field which are dual to forced fluid flows on the 4-dimensional boundary. In this paper, we generalise their work to arbitrary spacetime dimensions; we explicitly compute the dual bulk metric, the fluid dynamical stress tensor and Lagrangian to second order in a boundary derivative expansion.