  We outline a program for obtaining an action principle for dissipative fluid
dynamics by considering the holographic Wilsonian renormalization group applied
to systems with a gravity dual. As a first step, in this paper we restrict to
systems with a non-dissipative horizon. By integrating out gapped degrees of
freedom in the bulk gravitational system between an asymptotic boundary and a
horizon, we are led to a formulation of hydrodynamics where the dynamical
variables are not standard velocity and temperature fields, but the relative
embedding of the boundary and horizon hypersurfaces. At zeroth order, this
action reduces to that proposed by Dubovsky et al. as an off-shell formulation
of ideal fluid dynamics.
