Hydrodynamics of two-dimensional compressible fluid with broken parity: Variational principle and free surface dynamics in the absence of dissipation

Abstract

We consider compressible dissipationless fluids in two dimensions with broken parity symmetry (odd viscosity) and free surface boundary conditions. In the absence of shear viscosity, compression generates dissipationless vorticity near the boundary, enabling the application of a variational principle to derive a flow and dispersion relation for surface waves. We show that this leads to the emergence of spontaneously propagating chiral surface waves. The result is applicable to compressible fluids with broken parity symmetry ranging from electron fluids in graphene to out-of-equilibrium chiral active matter.

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