Universal Critical Velocity for the Onset of Turbulence of Oscillatory Superfluid Flow

The critical velocity v (c) for the onset of turbulent drag of small spheres oscillating in superfluid 4He is frequency dependent (omega/2 pi from 100 Hz to 700 Hz) and is described by , where beta similar to 1 depends on the coefficients of mutual friction. This agrees well with the data and implies that v (c) is a universal critical velocity that is independent of geometry, size, and surface properties of the oscillating body. This is confirmed by comparing our data on spheres with v (c) obtained with other oscillating structures by other groups. Numerical simulations indicate somewhat larger critical velocity, above which a rapid increase in vortex length is observed.