Statistics
Scientific paper
Jul 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006phdt.........3n&link_type=abstract
PhD Thesis: Proquest Dissertations And Theses 2006. Section 0262, Part 0759 130 pages; [Ph.D. dissertation].United States -- Wis
Statistics
Magnetohydrodynamics, Turbulence, Self-Excitation, Madison Dynamo Experiment
Scientific paper
Determining the onset conditions for magnetic field growth in magnetohydrodynamics is fundamental to understanding how astrophysical dynamos such as the Earth, the Sun, and the galaxy self-generate magnetic fields. The Madison Dynamo Experiment was constructed to explore the role of turbulence in changing these onset conditions for an impeller-driven flow of liquid sodium. The flow generates intermittent magnetic bursts with the spatial structure predicted from kinematic dynamo theory.
A model of the mean flow was constructed from laser Doppler velocimetry measurements of the flow in an identical-scale water experiment. A kinematic eigenvalue code predicted that the flow would generate a predominantly dipolar magnetic field perpendicular to the symmetry axis for sufficiently high impeller speeds. The flow amplifies the magnetic field by stretching field lines. The field lines are then twisted back onto themselves creating a feedback loop for dynamo growth. The same flow was generated in the sodium experiment and was found to amplify an applied magnetic field oriented perpendicular to the drive shaft axis of the experiment. The amplification increased with motor rotation rate as the induced field became more closely aligned with the applied field, though a reduction in the amplitude is attributed to an enhanced resistivity due to turbulent diffusion.
The turbulence was characterized by measurements of the velocity and magnetic power spectra. The velocity spectra have a Kolmogorov scaling. The wavenumber at which resistive dissipation range becomes dominant was observed to increase with flow speed indicating that smaller scale magnetic structures were generated. No amplification due to a small-scale dynamo was observed.
The intermittent bursts were analyzed using conditional averaging. The growth rate was found to increase linearly with impeller rotation rate resulting in stronger bursts. The average duration decreased so that the bursts continued to satisfy Poisson statistics; they remained rare, random events. The excitation of the bursts is attributed to modification of the dynamo threshold by large- scale velocity fluctuations. The results suggest that magnetic field generation in fully-developed turbulence is characterized by intermittent bursts caused by distortions of the flow profile with a minimal threshold for excitation.
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