Universal onset of quantum turbulence in oscillating flows and crossover to steady flows

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The critical velocity vc for the onset of quantum turbulence in oscillatory flows of superfluid helium is universal and scales as vc √κω, where κis the circulation quantum and ωis 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 vc ≈ √8κω/β, where β 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 vc changes when the steady case ω= 0 is approached. In that case vc scales as κ/R, where R is the size of the object.