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Forced fluid dynamics from gravity.

Authors :
Bhattacharyya, Sayantani
Loganayagam, R.
Minwalla, Shiraz
Nampuri, Suresh
Trivedi, Sandip P.
Wadia, Spenta R.
Source :
Journal of High Energy Physics; 2009, Vol. 2009 Issue 2, p018-018, 1p
Publication Year :
2009

Abstract

We generalize the computations of [1] to generate long wavelength, asymptotically locally AdS<subscript>5</subscript> solutions to the Einstein-dilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity , our solutions are dual, under the AdS/CFT correspondence, to arbitrary fluid flows in the boundary theory formulated on a weakly curved manifold with a prescribed slowly varying coupling constant. These solutions turn out to be parameterized by four-velocity and temperature fields that are constrained to obey the boundary covariant Navier Stokes equations with a dilaton dependent forcing term. We explicitly evaluate the stress tensor and Lagrangian as a function of the velocity, temperature, coupling constant and curvature fields, to second order in the derivative expansion and demonstrate the Weyl covariance of these expressions. We also construct the event horizon of the dual solutions to second order in the derivative expansion, and use the area form on this event horizon to construct an entropy current for the dual fluid. As a check of our constructions we expand the exactly known solutions for rotating black holes in global AdS<subscript>5</subscript> in a boundary derivative expansion and find perfect agreement with all our results upto second order. We also find other simple solutions of the forced fluid mechanics equations and discuss their bulk interpretation. Our results may aid in determining a bulk dual to forced flows exhibiting steady state turbulence. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
11266708
Volume :
2009
Issue :
2
Database :
Complementary Index
Journal :
Journal of High Energy Physics
Publication Type :
Academic Journal
Accession number :
86908615
Full Text :
https://doi.org/10.1088/1126-6708/2009/02/018