  Hydrodynamics is shown to induce non-Hermitian topological phenomena in
ordinary, passive soft matter. This is demonstrated for the first time by
subjecting a 2D elastic lattice to a low-Reynolds viscous flow. The interplay
of hydrodynamics and elasticity splits Dirac cones into bulk Fermi arcs,
pairing exceptional points with opposite half-integer topological charges. The
bulk Fermi arc is a generic hallmark of the system exhibited in all lattice and
flow symmetries. Analytic model and simulations explain how the emergent
singularities shape the spectral bands and give rise to a web of van Hove
singularity lines in the density of states. The present findings suggest that
non-Hermitian physics can be explored in a broad class of ordinary soft matter,
living and artificial alike, opening avenues for topology-based technology in
this regime.
