Odd surface waves

Two-dimensional isotropic fluids can possess an anomalous part of the viscous tensor known as odd or Hall viscosity. This peculiar viscosity does not lead to any dissipation in the fluid. I will describe the effects of the odd viscosity in incompressible fluids. In particular, I will present a solution corresponding to surface waves on a free boundaries of such fluids. In linear regime a new surface mode can exist even in the absence of external potential. The dispersion of this mode is $2\nu_o k |k|$. I will discuss the formation and the structure of an oscillating boundary layer accompanying odd surface waves. The weakly nonlinear and dispersive dynamics of surface waves is also derived. It is Hamiltonian. In some regime it is given by complex Burgers equation with imaginary viscosity which allows for exact solutions.