Phenomenology of nonrelativistic parity-violating hydrodynamics in 2+1 dimensions

Parity-violating fluids in two spatial dimensions can appear in a variety of contexts such as liquid crystal films, anyon fluids, and quantum Hall fluids. Nonetheless, the consequences of parity violation on the solutions to the equations of motion are largely unexplored. In this paper, we explore phenomenological consequences of parity violation through simple, illustrative examples. Although incompressible velocity fields are essentially unchanged by parity violation, we discuss examples where parity violation plays a role at boundaries, or in the dynamics of temperature. We then discuss types of compressible flows which only exist in a parity-violating fluid, including sound waves, and solitons in the dissipationless limit. We conclude with a discussion of some curious features in Rayleigh-Benard convection of a parity-violating fluid.