Emergent Kelvin waves in chiral active matter

Abstract

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.