Nonlinear dynamics in superfluid films

We have calculated the first non-linear corrections to the period shift andQ factor of a torsional oscillator containing a film of helium. To do so we have solved the Fokker Planck equation for the distribution of vortex pairs in the presence of an oscillating superfluid velocity field. The non-linear response is predicted to be proportional tov n 2 for low values of the normal fluid velocity,vn, which is in good agreement with the experimental results of Adams and Glaberson. For temperatures above the Kosterlitz Thouless transition temperature,TKT, the ratio of the correlation length ξ+ to the diffusion length becomes important in describing the temperature dependence of the non-linear response. We predict how the non-linear response depends on this ratio in the region where the ratio is large.