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?
Perhaps I am just displaying my ignorance on the subject, but I will stick out my neck and try to answer - I am grateful for comments, especially if my picture is wrong.
ad first question: I would have pictured the dissipation as follows. By switching on some perturbation you bring the black hole into an excited state that can be treated perturbatively as long as it is a small enough excitation. This then leads to quasi-normal ringing of the black hole. The perturbed black hole state falls back to the unperturbed black hole state by emission of gravitational waves towards the AdS boundary. Thus, the dissipation process on the gravity side rather seems to be energy transported from the UV to the IR.
ad second question: By the UV/IR connection the quasi-normal ringing on the gravity side should on the fluid side correspond to energy in the IR being dissipated into the UV. I would have thought that this is precisely what happens in a viscous fluid: you have some long wavelength motion that gets decelerated due to friction, which is basically small wavelength excitations that then thermalize with the heat bath.
References on quasi-normal modes:
In AdS: hep-th/9909056 In general relativity: gr-qc/9909058