  We generalise the computations of arXiv:0712.2456 to generate long
wavelength, asymptotically locally AdS_5 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 parametrised 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_5 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.
