We formulate a Lagrangian hydrodynamics including shear and bulk viscosity in the presence of spin density, and investigate it using the linear response functional formalism. The result is a careful accounting of all sound and vortex interactions close to local equilibrium. In particular, we demonstrate that the mixing of sound waves and vortices via polariыation, first observed in the ideal fluid limit, extends to the shear mode once dissipative effects are included. Once causal relaxational dynamics is included, this effect, seemingly puzzling because it results in a non-dissipative coupling between a transient mode to an equilibrium quantity, can be understood as a competition between the Israel-Stewart and the polarization relaxation timescale.