Universal Onset of Quantum Turbulence in Oscillating Flows and Crossover to Steady Flows

The critical velocity nu(c) for the onset of quantum turbulence in oscillatory flows of superfluid helium is universal and scales as nu(c) similar to root kappa omega, where kappa is the circulation quantum and omega is the oscillation frequency. This result can be derived from a general argument based on the "superfluid Reynolds number". Only the numerical prefactor may depend somewhat on the geometry of the oscillating object because the flow velocity at the surface of the object may differ from the velocity amplitude of the body. A more detailed analysis derived from the dynamics of the turbulent state gives nu(c) similar to root 8 kappa omega/beta, where beta similar to 1 depends on the mutual friction parameters. This universality is compared with the recently discovered universality of classical oscillatory flows. We also discuss the effect of remanent vorticity on the onset of quantum turbulence. Finally, by employing the "superfluid Reynolds number" again, we argue how nu(c) changes when the steady case omega = 0 is approached. In that case nu(c) scales as kappa/R, where R is the size of the object.