  The fluid-gravity correspondence provides us with explicit spacetime metrics
that are holographically dual to (non-)relativistic nonlinear hydrodynamics.
The vacuum Einstein equations, in the presence of a Killing vector, possess
solution-generating symmetries known as spacetime Ehlers transformations. These
form a subgroup of the larger generalized Ehlers group acting on spacetimes
with arbitrary matter content. We apply this generalized Ehlers group, in the
presence of Killing isometries, to vacuum metrics with hydrodynamic duals to
develop a formalism for solution-generating transformations of Navier-Stokes
fluids. Using this we provide examples of a linear energy scaling from RG flow
under vanishing vorticity, and a set of Z_2 symmetries for fixed viscosity.
