Transition from Ekman flow to Taylor vortex flow in superfluid helium

TL;DR

This paper numerically investigates the transition from Ekman to Taylor vortex flow in superfluid helium, revealing unique low-Reynolds number behaviors and confirming stability theory at high aspect ratios.

Contribution

It provides the first detailed numerical analysis of flow transitions in superfluid helium, highlighting differences from classical fluids and validating theoretical predictions.

Findings

Flow behavior differs significantly from classical fluids at low temperatures.

Transition thresholds align with linear stability theory at high aspect ratios.

Flow patterns depend on temperature and aspect ratio.

Abstract

By numerically computing the steady axisymmetric flow of helium II confined inside a finite aspect ratio Couette annulus, we determine the transition from Ekman flow to Taylor vortex flow as a function of temperature and aspect ratio.We find that the low-Reynolds number flow is quite different to that of a classical fluid, particularly at lower temperatures.At high aspect ratio our results confirm the existing linear stability theory of the onset of Taylor vortices, which assumes infinitely long cylinders.