The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
arXiv:0810.1545 · doi:10.1088/1126-6708/2009/08/059
Abstract
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.
22+1 pages, 3 figures, JHEP format ; v2 : References and minor clarifications added, v3: Minor clarifications
References in corpus (8)
- Nonlinear Fluid Dynamics from Gravity
- Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
- Viscosity, Black Holes, and Quantum Field Theory
- Entropy Current in Conformal Hydrodynamics
- Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
- The geometry of Schrödinger symmetry in non-relativistic CFT
- Forced Fluid Dynamics from Gravity
- Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations