Formation and structure of a spontaneous geostrophic edge current in the steady state of a chiral active fluid

Chiral active fluids are composed of particles that convert energy into rotational motion in a preferred direction. Their unforced steady states violate time-reversal and parity symmetry, leading to a taxonomy of exotic transport phenomena unobservable in ordinary passive fluids whose quiescent states are in equilibrium. The most famous such phenomenon is the odd viscosity, linking forcing to fluid motion in an orthogonal direction. Microscopically, chiral active fluids are characterized by the local injection of spin angular momentum. However, the free spin of individual constituent particles is frustrated by interparticle interaction at finite density. With a combination of theory and simulation, we show that this frustration, along with angular momentum conservation, leads to the spontaneous formation of a boundary current whose direction is determined by the chirality of the system. We further develop hydrodynamic equations governing our model system and use these equations to derive the structure of this boundary current. The hydrodynamic results are in excellent agreement with the profile observed in simulations, allowing us to extract estimates of the odd and shear viscosities governing the flow. We finally demonstrate that this boundary flow is an exact mathematical analogy of an oceanographic current known as a geostrophic coastally bound current, which forms when buoyant water flows between oceanographic basins or from estuaries into coastal environments.