Free surface boundary dynamics of compressible and dissipationless fluids with Hall viscosity

In this talk, we consider non-dissipative and compressible two-dimensional broken parity fluids with odd viscosity and magnetic field with a free surface boundary condition. We solve the linearized hydrodynamic equations for the deepwater case and derive the dispersion of chiral surface waves. We show that in the long-wavelength limit the flow profile exhibits an oscillating vortical boundary layer near the free surface. The thickness of the layer is controlled by the length scale given by the ratio of odd viscosity to the sound velocity. In the incompressible limit, the vortical boundary layer becomes singular with the vorticity within the layer diverging as the velocity of sound. The boundary layer is formed by odd viscosity coupling the divergence of velocity to vorticity. It results in non-trivial chiral free surface dynamics even in the absence of external forces. The structure of the odd viscosity induced boundary layer is very different from the conventional free surface boundary layer associated with dissipative shear viscosity.