  We study universal spatial features of certain non-equilibrium steady states
corresponding to flows of strongly correlated fluids over obstacles. This
allows us to predict universal spatial features of far-from-equilibrium
systems, which in certain interesting cases depend cleanly on the hydrodynamic
transport coefficients of the underlying theory, such as $\eta/s$, the shear
viscosity to entropy density ratio. In this work we give a purely
field-theoretical definition of the spatial collective modes identified earlier
and proceed to demonstrate their usefulness in a set of examples, drawing on
hydrodynamic theory as well as holographic duality. We extend our earlier
treatment by adding a finite chemical potential, which introduces a
qualitatively new feature, namely damped oscillatory behavior in space. We find
interesting transitions between oscillatory and damped regimes and we consider
critical exponents associated with these. We explain in detail the numerical
method and add a host of new examples, including fully analytical ones. Such a
treatment is possible in the large-dimension limit of the bulk theory, as well
as in three dimensions, where we also exhibit a fully analytic non-linear
example that beautifully illustrates the original proposal of spatial
universality. This allows us to explicitly demonstrate how an infinite tower of
discrete modes condenses into a branch cut in the zero-temperature limit,
converting exponential decay into a power law tail.
