Dynamical scaling of the critical velocity for the onset of turbulence in oscillatory superflows

TL;DR

This paper demonstrates that the critical velocity for turbulence onset in oscillatory superfluid helium flows scales with the square root of frequency, derived through dynamical vortex scaling laws, confirming earlier qualitative models.

Contribution

The work provides a rigorous derivation of the v_c ~ sqrt(omega) scaling law using dynamical vortex equations, extending previous qualitative approaches.

Findings

Critical velocity scales as sqrt(omega).

Scaling law is derived rigorously from vortex dynamics.

Universal behavior confirmed across geometries.

Abstract

The critical velocity v_c for the onset of turbulence in oscillatory flows of superfluid helium is known to depend on the oscillation frequency omega, namely v_c ~ sqrt(kappa*omega) where kappa is the circulation quantum. Only the numerical prefactor may have some geometry dependence. This universal behaviour was described earlier qualitatively either by employing the superfluid Reynolds number or by extending known dc vortex dynamics to ac flow. In our present work we emphasize that v_c(omega) ~ sqrt(omega) can also be derived rigorously by means of dynamical scaling of equations of vortex dynamics as pointed out by Kotsubo and Swift already two decades ago.