Hydrodynamic vortices and their gravity duals

Abstract

In this talk we review analytical and numerical studies of hydrodynamic vortices in conformal fluids and their gravity duals. We present two conclusions. First, (3+1)-dimensional turbulence is within the range of validity of the AdS/hydrodynamics correspondence. Second, the local equilibrium of the fluid is equivalent to the ultralocality of the holographic correspondence, in the sense that the bulk data at a given point is determined, to any given precision, by the boundary data at a single point together with a fixed number of derivatives. With this criterion we see that the cores of hot and slow (3+1)-dimensional conformal generalizations of Burgers vortices are everywhere in local equilibrium and their gravity duals are thus easily found. On the other hand local equilibrium breaks down in the core of singular (2+1)-dimensional vortices, but the holographic correspondence with Einstein gravity may be used to define the boundary field theory in the region in which the hydrodynamic description fails.

Holographic Path to the Turbulent Side of Gravity

“…Naturally, as already pointed out in [19], it would be very useful to develop a spacetime definition of the Reynolds number. This would provide an intrinsic way to predict the onset of turbulence in gravity and could thus be applied in broader contexts.…”

“…For instance, it provides motivation to look for scenarios where slowly decaying perturbations might give rise to interesting non-linear interactions. Finally, insights from turbulence may shed new light on particular systems known to exhibit related behavior, such as the chaotic behavior of spacelike singularities in early-universe mixmaster dynamics [19].…”

“…On the fluid side, such properties are conveniently captured by the Reynolds number (although, as noted above, a relativistic generalization is desirable for relativistic fluids). Thus it would be very interesting to obtain a geometrical realization of the Reynolds number, in order to predict the onset of turbulence in gravity [19].…”

“…These should not be confused with "black funnels"[40], which are bulk black holes with a horizon that connects to the conformal boundary of the spacetime. Evslin[19] has conjectured these black funnels to correspond to singular fluid vortices 12. For some alternative discussions, see, e.g.,[41,42].…”