NUMERICAL SIMULATION AND EXPERIMENTAL VISUALISATION OF QUANTUM TURBULENCE IN THE ZERO TEMPERATURE LIMIT

Abstract

Numerical simulations of vortex lines in flows of superfluid He$^4$, in the zero-temperature limit, were produced in channels with two limits of vortex pinning: (i) the rough case; the flat channel walls were assumed to be microscopically rough on the scale of the discrete spatial resolution of the simulation, vortices were permanently pinned at the surface until freeing themselves through a reconnection with their image; (ii) the sliding case; the channel walls were weakly corrugated with micron-scale amplitude, vortices could slide along the surface continuously pumping Kelvin waves into the vortex line damped by a drag interaction with a vortex tangle. Numerical modelling was conducted using the vortex filament model. Isolated vortex lines demonstrated the stream-wise friction force was independent of the flow velocity in the rough limit and held a linear relationship in the sliding limit. The spectrum of Kelvin waves populating vortices were identified by fast Fourier transform of the lines' shapes. Velocity profiles of coarse-grained vortex tangles with rough pinning resembled the Poiseuille profile of classical laminar flows, however, exhibited a non-zero slip velocity at the walls with value similar to the critical velocity for sustained turbulence. Sustained tangles exhibited a friction force which scaled linearly with flow velocity. An effective kinematic viscosity for momentum transfer through the vortex tangle was found $\nu_m = (0.12\pm0.01)\kappa$, for corresponding Reynolds numbers below 150. A superfluid He$^4$ pipe flow apparatus was designed and calibrated to measure the pressure drop, thus friction force, in the zero-temperature limit for direct comparison with these simulations. Additionally, an experiment was undertaken to visualise the interactions of fluorescent micron-scale tracer particles and quantum vortices in the temperature range 0.14--1.20 K. A single-target particle tracking algorithm was implemented to trace the microsphere's motion through superfluid He$^4$. In the zero-temperature limit most observed particle motion was too fast to faithfully track. A particle masking routine was added to enhance tracking and allowed identification of particle velocity distributions at the lowest achieved temperatures.

Date of Award	20 Mar 2025
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Andrei Golov (Main Supervisor) & Paul Walmsley (Co Supervisor)