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

Abstract

The critical velocity v_c for the onset of quantum turbulence in oscillatory flows of superfluid helium is universal and scales as v_c \sim \sqrt{\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 v_c \approx \sqrt{8\kappa\omega/\beta}, where \beta \sim 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 v_c changes when the steady case \omega = 0 is approached. In that case v_c scales as \kappa/R, where R is the size of the object.