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{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 v_c \approx \sqrt{8κω/β}, where β\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 ω= 0 is approached. In that case v_c scales as κ/R, where R is the size of the object.

3 pages, 1 figure

References in corpus (4)

• The Generation of Turbulence by Oscillating Structures in Superfluid Helium at Very Low Temperatures
• A Universality in Oscillating Flows
• Universal Critical Velocity for the Onset of Turbulence of Oscillatory Superfluid Flow
• On the Transition to Turbulence of Oscillatory Flow of Liquid Helium-4

Cited by in corpus (5)

• Theoretical analysis of quantum turbulence using the Onsager "ideal turbulence" theory
• Statistics of Intermittent Switching between Potential Flow and Turbulence around an Oscillating Sphere in Superfluid 4He below 0.5 K
• On the Transition from Potential Flow to Turbulence Around a Microsphere Oscillating in Superfluid ^4He
• Dynamical scaling of the critical velocity for the onset of turbulence in oscillatory superflows
• Vortex Shedding from an Object Moving in Superfluid ${}^4$He at mK Temperatures and in a Bose-Einstein Condensate