Instability of vortex array and transitions to turbulent states in rotating helium II

TL;DR

This paper investigates the stability of vortex arrays in rotating superfluid helium II under axial flow, revealing Kelvin wave instabilities leading to turbulence and explaining experimental observations.

Contribution

It provides a numerical analysis of vortex array instabilities in superfluid helium II, identifying Kelvin wave growth and vortex reconnections as key mechanisms, and offers a theoretical explanation for higher flow instabilities.

Findings

Kelvin waves become unstable and grow in amplitude.

Vortex reconnections lead to a turbulent vortex tangle.

Results align well with experimental observations.

Abstract

We consider superfluid helium inside a container which rotates at constant angular velocity and investigate numerically the stability of the array of quantized vortices in the presence of an imposed axial counterflow. This problem was studied experimentally by Swanson {\it et al.}, who reported evidence of instabilities at increasing axial flow but were not able to explain their nature. We find that Kelvin waves on individual vortices become unstable and grow in amplitude, until the amplitude of the waves becomes large enough that vortex reconnections take place and the vortex array is destabilized. The eventual nonlinear saturation of the instability consists of a turbulent tangle of quantized vortices which is strongly polarized. The computed results compare well with the experiments. Finally we suggest a theoretical explanation for the second instability which was observed at higher values of the axial flow.