Note on the superfluid Reynolds number for turbulent flow of superfluid $^4$He around an oscillating sphere

TL;DR

This paper introduces a simple expression for the superfluid Reynolds number in turbulent superfluid helium-4 flow, linking it to vortex ring shedding during oscillation.

Contribution

It presents a novel, straightforward way to relate the superfluid Reynolds number to vortex ring shedding in oscillating superfluid helium-4.

Findings

Re_s is proportional to vortex rings shed per oscillation half-period

Provides a simple expression for superfluid Reynolds number

Links vortex dynamics to flow turbulence in superfluid helium

Abstract

The superfluid Reynolds number $Re_s = (v - v_c) \,D/ \kappa$ can be expressed simply by the number of vortex rings that are shed during a half-period of the oscillation.