NONLINEAR DYNAMICS IN SUPERFLUID FILMS

We have calculated the first non-linear corrections to the period shif t and Q factor of a torsional oscillator containing a film of helium. To do so we have solved the Fokker Planck equation for the distributio n of vortex pairs in the presence of an oscillating superfluid velocit y field. The non-linear response is predicted to be proportional to v( n)2 for low values of the normal fluid velocity, v(n), which is in goo d agreement with the experimental results of Adams and Glaberson. For temperatures above the Kosterlitz Thouless transition temperature, T(K T), the ratio of the correlation length zeta+ 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 thi s ratio in the region where the ratio is large.