Odd viscosity in two dimensional incompressible fluids

In everyday fluids, the viscosity is resistance to flow and is dissipative, but a quantum Hall (QH) fluid at zero temperature has non-dissipative viscosity dubbed `odd-viscosity'. In this talk, I will present observable consequences of parity-violating odd viscosity term in incompressible 2+1D hydrodynamics. For boundary conditions depending on the velocity field (flow) alone we show that: (i) The fluid flow quantified by the velocity field is independent of odd viscosity, (ii) The force acting on a closed contour is independent of odd viscosity, and (iii) The odd viscosity part of torque on a closed contour is proportional to the rate of change of area enclosed by the contour with the proportionality constant being twice the odd viscosity. The last statement allows us to define a measurement protocol of "odd viscostance" in analogy to Hall resistance measurements. We also consider no-stress boundary conditions which explicitly depend on odd viscosity. I will discuss effects of odd viscosity in classic hydrodynamics problems with no-stress boundary conditions, namely, bubble in a planar Stokes flow and surface gravity waves.