Dynamics of quantized vortices in applied flow in superfluid 3He-B

Robert Jan de Graaf

    Research output: ThesisDoctoral ThesisCollection of Articles


    This thesis is mostly focussed on studies of dynamics of superfluid ³He-B at temperatures below 0.4Tc where the flow of quantized vortex lines was expected to be generally turbulent. The damping in vortex motion changes many orders of magnitude in a small temperature interval making vortices in superfluids an ideal tool to study turbulence. The quantum nature of vortices in superfluids allows for exotic hydrodynamics that does not exist in classical fluids. Earlier research had showed that vortices become unstable and lead to turbulence when the superfluid Reynolds number exceeds unity. The question remained open whether vortical flow is inherently unstable at lower temperatures. This thesis addresses issues surrounding the instability of quantized vortices in applied flow in the zero-temperature limit. Using the non-invasive nuclear magnetic resonance measurement technique, we have studied the dynamics of vortices in transient states during spin-up experiments where the rotation velocity of the system changes in a step-like manner. We found transition temperatures where the vortices connected to the cylindrical container become unstable and, ultimately, start a turbulent burst of vortex formation. This is in contrast to the laminar motion at higher temperatures, where the vortex ends smoothly slide in helical motion on the cylindrical surface. The exact conditions for this onset temperature to turbulence are established in terms of the applied flow, and the perturbation of the superfluid state by so-called seed vortices. The spin-up and spin-down experiments in the zero-temperature limit show different vortex dynamics. The vortex motion in applied flow is laminar for a cylindrical container, while in a cubical geometry the motion is expected to be partly turbulent. Our experiments on turbulent front propagation after injection of seed vortices from the AB-phase boundary (via the Kelvin-Helmholtz instability) into the rotating Landau state show a change over from quasi-classical turbulence at high temperatures, to quantum turbulence in the low temperature regime where the energy cascade of Kelvin wave excitations starts to contribute to the dissipative process. The effect of a bottleneck in this energy cascade is expressed in the front propagation velocity. The contribution of the density anisotropy to the textural energy of the superfluid in rotation is measured from the high to the zero-temperature limit. Comparison with theory allows determination of the superfluid energy gap. We have mapped the superfluid order parameter flare out textures in terms of applied flow and temperature. A quartz tuning fork with a high quality factor has been studied in superfluid ³He-B. The device is found to be an excellent tool to measure temperature, pressure and viscosity. In the zero-temperature limit, where other temperature measurement devices start to saturate, the fork's sensitivity increases due to the exponential dependence on the quasiparticle density.
    Translated title of the contributionDynamics of quantized vortices in applied flow in superfluid 3He-B
    Original languageEnglish
    QualificationDoctor's degree
    Awarding Institution
    • Aalto University
    • Kaivola, Matti, Supervising Professor
    • Krusius, Franz, Supervising Professor
    Print ISBNs978-952-60-4107-0
    Electronic ISBNs978-952-60-4108-7
    Publication statusPublished - 2011
    MoE publication typeG5 Doctoral dissertation (article)


    • superfluids
    • helium
    • vortex dynamics
    • front propagation
    • aminar
    • turbulence
    • Reynolds number
    • nuclear magnetic resonance
    • quartz tuning fork


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