  The phenomenological equations of hydrodynamics describe emergent behavior in
many body systems. Their forms and the associated phenomena are well
established when the quiescent state of the system is one of thermodynamic
equilibrium, yet away from equilibrium relatively little is firmly established.
Here, we deduce directly from first principles the hydrodynamic equations for a
system far from equilibrium, a chiral active fluid in which both parity and
time-reversal symmetries are broken. With our theory, we rationalize the
emergence of a spontaneous boundary current in the confined fluid, a feature
forbidden at equilibrium, which allows us to extract estimates of transport
coefficients that we favorably compare to forced flows. The hydrodynamic
solution reveals that the boundary current is analogous to a quasigeostrophic
coastal current, a well known phenomenon in oceanography. Such currents are
conjugate to a class of chiral waves called Kelvin waves. Motivated by this
analogy, we demonstrate that an acoustic chiral Kelvin wave mode also exists in
confined chiral active matter in the absence of an imposed rotation,
originating from the spontaneous emergence of a Coriolis-like parameter in the
bound modes of a chiral fluid.
