Universal Critical Velocity for the Onset of Turbulence of Oscillatory Superfluid Flow

TL;DR

This paper demonstrates that the critical velocity for the onset of turbulence in oscillatory superfluid flow is universal, depending only on frequency and fundamental constants, regardless of the object's geometry or surface properties.

Contribution

It introduces a universal formula for the critical velocity in oscillatory superfluid flow, supported by experimental data and numerical simulations, unifying previous disparate observations.

Findings

Critical velocity scales as sqrt(kappa*omega)

Universal critical velocity independent of object geometry

Numerical simulations show higher critical velocities

Abstract

The critical velocity vc for the onset of turbulent drag of small spheres oscillating in superfluid 4He is frequency dependent (omega/2pi from 100 Hz to 700 Hz) and is described by vc = 2.6sqrt(kappa*omega), where kappa is the circulation quantum. A qualitative analysis based on a recent theory of the onset of superfluid turbulence gives vc = sqrt(8*kappa*omega/beta), where beta is of order 1 and depends on the coefficients of mutual friction. This agrees well with the data and implies that vc is a universal critical velocity that is independent of geometry, size, and surface properties of the oscillating body. This is confirmed by comparing our data on spheres with vc obtained with other oscillating structures by other groups. Numerical simulations indicate somewhat larger critical velocity, above which a rapid increase in vortex length is observed.