  We study the response of a Dirac fluid to electric fields and thermal
gradients at finite wave-numbers and frequencies in the hydrodynamic regime. We
find that non-local transport in the hydrodynamic regime is governed by
infinite set of kinetic modes that describe non-collinear scattering events in
different angular harmonic channels. The scattering rates of these modes
$\tau_{m}^{-1}$ increase as $\|m\|$, where $m$ labels the angular harmonics. In
an earlier publication, we pointed out that this dependence leads to anomalous,
L\'evy-flight-like phase space diffusion (Phys. Rev. Lett. 123, 195302 (2019)).
Here, we show how this surprisingly simple, non-analytic dependence allows us
to obtain exact expressions for the non-local charge and electronic thermal
conductivities. The peculiar dependence of the scattering rates on $m$ also
leads to a non-trivial structure of collective excitations: Besides the well
known plasmon, second sound and diffusive modes, we find non-degenerate damped
modes corresponding to excitations of higher angular harmonics. We use these
results to investigate the transport of a Dirac fluid through Poiseuille-type
geometries of different widths, and to study the response to surface acoustic
waves in graphene-piezoelectric devices.
