Formation and decay of vorticity in coupled helium-II flow

The kinematic viscosity of helium II below the transition temperature can be defined with the total density of the liquid or the normal-fluid density alone. These two definitions have very different temperature dependences. In this work we considered the decay of Gaussian distributions of vorticity in helium II using the two fluid Hall-Vinen-Bekharevich-Khalatnikov equations. Our calculation shows that in these two-dimensional axisymmetric flows both fluids decay together with a viscous time scale set by the total fluid density and not by the normal-fluid density alone. We also considered the spin-up of each fluid and observed that for all initial conditions considered both fluids tend towards a matched vorticity state