# Scale dependence of energy dissipation in viscous flow via AdS/CFT

The famous AdS/CFT calculation of the shear viscosity/entropy ratio for strongly coupled $N=4$ SYM relates the shear viscosity to the absorption cross section for fluctuations of the metric onto a black hole in AdS which in turn can be related to the absorption cross section for a massless scalar field. On the AdS side it seems clear that dissipation and relaxation back to an equilibrium configuration after a disturbance means that the disturbance has been absorbed by the black hole, and this would seem to imply that the disturbance propagates from small $z$ to large $z$ in Poincare coordinates where $z \rightarrow 0$ is the UV boundary. That is, the energy of the disturbance propagates from the UV to the IR where it is dissipated. First question: is this the right physical picture? Second question: this seems to imply on the CFT side that the dissipation of energy due to shear viscosity also involves a transfer of energy from the UV to the IR. Is this consistent with what is known in fluid mechanics for viscous flow? If so, can you provide a reference?

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 I don't know the answer in general, but if you allow me quick stream of consciousness comment: I remember that in turbulent flow the physical picture is the opposite - energy is transferred from large scale structures to small ones, and is dissipated at the UV. – user566 Feb 15 '11 at 5:02 But turbulent flow in two (spatial) dimensions goes the other way, from UV to IR, right? (Doesn't seem directly relevant, but at least shows this direction can be physically sensible....) – Matt Reece Feb 15 '11 at 5:34 Just relying on vague and not so recent memory, you may be right. My comment at least is not directly relevant, the fluid flow modelled by AdS is not turbulent. Hopefully someone with experience in fluid dynamics will help. – user566 Feb 15 '11 at 5:47 Dear @Moshe, in your 1st comment, are you describing the Hawking radiation in the CFT variables? If the viscosity is linked to the absorption by a black hole, how could Jeff's translation go wrong? – Luboš Motl Feb 15 '11 at 6:52 @Lubos: I was talking about the phenomenology of turbulent flow, as seen for example in wind tunnels. I don't see anything wrong with Jeff's reasoning, so I'm also puzzled - but there could be a simple and disappointing explanation. – user566 Feb 15 '11 at 7:00