  In this paper we show that an incompressible three dimensional or
compressible in two dimensions odd viscous liquid gives rise to both
oscillatory and evanescent waves or a combination of the two. By evanenscent we
mean that along at least one of the spatial directions the velocity field, or
an envelope thereof, increases or decreases exponentially. Thus, these latter
waves can become prominent in the vicinity of a solid boundary. Helicity is
conserved in such a flow composed of plane-polarized waves. The combination of
rotation and odd viscosity gives rise to some unconventional behavior. In
certain parameter regimes, plane polarized inertial waves may acquire a
non-convex dispersion relation, known to become associated with oscillatory
soliton tails and dispersive shocks in the presence of nonlinear terms. Maxima
of the group velocity appear at angles $\neq\frac{\pi}{2}$ between the axis of
rotation and the wavevector. The corresponding direction of energy wave-packet
propagation and helical particle paths can thus be chosen at will by a prudent
election of odd viscosity and angular velocity parameter regimes. We show that
recent numerical experiments on a two-dimensional compressible odd viscous
liquid establishing the existence of topological waves near a boundary can be
understood as evanescent inertial waves described by our formulation. The
presence or absence of scattering of density waves in such a liquid is
interpreted with respect to the motion of a disturbance with subsonic or
supersonic speeds, respectively, the delineation of which is caused by odd
viscosity coupled to rigid rotation-mediated renormalization of the speed of
sound. This offers an explanation alternative to the one based on topological
numbers.
