Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-10-09
JHEP 0908:059,2009
Physics
High Energy Physics
High Energy Physics - Theory
22+1 pages, 3 figures, JHEP format ; v2 : References and minor clarifications added, v3: Minor clarifications
Scientific paper
10.1088/1126-6708/2009/08/059
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to `accelerated boost' symmetries of the Navier-Stokes equations, uncovering a possibly new conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.
Bhattacharyya Sayantani
Minwalla Shiraz
Wadia Spenta R.
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