The wake of a sphere in a chiral fluid*

Systems composed of spinning particles or driven by a magnetic field break mirror symmetry at the microscopic level. These chiral fluids can be described by adding additional so-called "odd" viscosities, which do not dissipate energy, in the Navier-Stokes equation. Here, we ask: how does odd viscosity affect the wake of a sphere as the Reynolds number increases? In ordinary fluids, the wake undergoes several bifurcations, first from an axisymmetric to a non-axisymmetric steady state, and then to a state where it periodically sheds vortices, similar to the von Karman vortex street familiar from everyday fluid flows. Using a combination of numerical and analytical methods, we describe the transitional flow regime in a chiral fluid. We find that odd viscosity reshapes the vortex structure of the wake, which in turn affects the onset and nature of the periodic vortex shedding state. Our work sheds light on the transition to turbulence in chiral fluids, a regime that could be realized experimentally in collections of spinning inertial particles.