The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
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Experiments on Vortex Dynamics in Superfluid 3He

Antti Finne

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics for public examination and debate in Auditorium F1 at Helsinki University of Technology (Espoo, Finland) on the 23rd of September, 2005, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-7831-6)   [750 KB]
Dissertation is also available in print (ISBN 951-22-7830-8)

Abstract

There are two stable isotopes of helium: helium-3 and helium-4. Both exhibit superfluidity at low temperatures, helium-3 at around 1 mK. The superfluidity brings some special features to the fluid, such as the possibility of frictionless mass flow and quantization of flow through vortex lines. This thesis consists of experiments performed on superfluid helium-3 under rotation, and on the vortex lines the rotation induces. The cylindrical sample is probed using nuclear magnetic resonance (NMR) and there is a possibility to stabilize two superfluid phases, the A phase and the B phase, simultaneously in the sample. We study two aspects: the dynamics of the phase boundary between the A and the B phases, and turbulent vortex dynamics in the B phase.

When a sample which consists of both the A and the B phases is rotated, a velocity difference in the superfluid components can form across the phase boundary. At a sufficiently high velocity the boundary becomes unstable towards wave formation, analogously to the Kelvin-Helmholtz instability in classical hydrodynamics (e.g. waves form on water while wind blows over the surface). In regular fluids their viscosity affects the instability, these experiments are the first demonstration of the instability in superfluids. We present measurements on the criterion for the instability, and how vortex lines cross the phase boundary as a result. The instability turned out to provide unprecedented flexibility in vortex injection into the B phase and is used in the study of turbulent vortex dynamics.

Many questions remain unanswered regarding classical turbulence. In a superfluid, turbulence is seen as a chaotic motion of vortex lines. Turbulence has been studied intensively in superfluid helium-4, the measurements in this thesis are one of the first to show turbulent flow in the B phase of helium-3. Experiments in helium-3 give new insight into turbulent vortex dynamics since the two fluids differ in their hydrodynamic properties, for example, in terms of damping of vortex motion, vortex formation, and the dynamics of the normal fluid background. We study which effects are important in the formation of a turbulent vortex network, how the vortex lines spread into the vortex free region, and finally how they relax into the equilibrium state. We identify a similarity parameter for the flow in an analogous fashion to the Reynolds number in normal fluid dynamics. Unlike in regular fluids, the hydrodynamic transition between regular and turbulent vortex dynamics appears to be controlled by intrinsic parameters only.

This thesis consists of an overview and of the following 13 publications:

  1. A. Finne, L. Grönberg, R. Blaauwgers, V. B. Eltsov, G. Eska, M. Krusius, J. J. Ruohio, R. Schanen, and I. Suni, Superconducting Nb-film LC resonator, Review of Scientific Instruments 72 (9), 3682 (2001).
  2. R. Blaauwgeers, V. B. Eltsov, G. Eska, A. P. Finne, R. P. Haley, M. Krusius, J. J. Ruohio, L. Skrbek, and G. E. Volovik, Shear flow and Kelvin-Helmholtz instability in superfluids, Physical Review Letters 89, 155301 (2002). © 2002 American Physical Society. By permission.
  3. M. Krusius, A. P. Finne, R. Blaauwgeers, V. B. Eltsov, and G. E. Volovik, Vortex line connections across the AB interface in superfluid 3He, Physica B 329-333, 91 (2003).
  4. V. B. Eltsov, R. Blaauwgeers, A. P. Finne, M. Krusius, J. J. Ruohio, and G. E. Volovik, Instability of AB interfaces of different shapes in rotating 3He, Physica B 329-333, 96 (2003).
  5. R. Blaauwgeers, S. Boldarev, V. B. Eltsov, A. P. Finne, and M. Krusius, Superfluid He in rotation: single-vortex resolution and requirements on rotation, Journal of Low Temperature Physics 132, 263 (2003). © 2003 Springer Science+Business Media. By permission.
  6. R. Hänninen, R. Blaauwgeers, V. B. Eltsov, A. P. Finne, M. Krusius, E. V. Thuneberg, and G. E. Volovik, Structure of the surface vortex sheet between two rotating 3He superfluids, Physical Review Letters 90, 225301 (2003). © 2003 American Physical Society. By permission.
  7. A. P. Finne, T. Araki, R. Blaauwgeers, V. B. Eltsov, N. B. Kopnin, M. Krusius, L. Skrbek, M. Tsubota, and G. E. Volovik, An intrinsic velocity-independent criterion for superfluid turbulence, Nature 424, 1022 (2003).
  8. A. P. Finne, V. B. Eltsov, R. Blaauwgeers, Z. Janu, M. Krusius, and L. Skrbek, Time-of-flight measurements on quantized vortex lines in rotating 3He-B, Journal of Low Temperature Physics 134, 375 (2004). © 2004 Springer Science+Business Media. By permission.
  9. A. P. Finne, S. Boldarev, V. B. Eltsov, and M. Krusius, Vortex formation in neutron-irradiated rotating superfluid 3He-B, Journal of Low Temperature Physics 135, 479 (2004). © 2004 Springer Science+Business Media. By permission.
  10. A. P. Finne, S. Boldarev, V. B. Eltsov, and M. Krusius, Measurement of turbulence in superfluid 3He-B, Journal of Low Temperature Physics 136, 249 (2004). © 2004 Springer Science+Business Media. By permission.
  11. A. P. Finne, S. Boldarev, V. B. Eltsov, and M. Krusius, Phase diagram of turbulence in superfluid 3He-B, Journal of Low Temperature Physics 138, 567 (2005). © 2005 Springer Science+Business Media. By permission.
  12. A. P. Finne, V. B. Eltsov, G. Eska, R. Hänninen, J. Kopu, M. Krusius, E. V. Thuneberg, and M. Tsubota, Vortex multiplication in applied flow: the precursor to superfluid turbulence, Helsinki University of Technology, Low Temperature Laboratory publications, Report TKK-KYL-014 (2005).
  13. A. P. Finne, V. B. Eltsov, R. Hänninen, J. Kopu, N. B. Kopnin, M. Krusius, E. V. Thuneberg, M. Tsubota, and G. E. Volovik, Vortex formation and dynamics in rotating superfluid 3He-B below 0.6 Tc, Helsinki University of Technology, Low Temperature Laboratory publications, Report TKK-KYL-015 (2005).

Keywords: superfluid, helium-3, vortex dynamics, turbulence, Kelvin-Helmholtz instability

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© 2005 Helsinki University of Technology

Last update 2011-05-26