2006/11/17 by Günther Rüdiger, G. Ruediger, M. Schultz +4 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Condensed matter physics #Couette flow #Dissipative system #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geomagnetism and Paleomagnetism Studies #Geometry #Hartmann number #Heat transfer #Instability #Magnetic Prandtl number #Magnetic Reynolds number #Magnetic field #Magnetohydrodynamics #Mathematics #Mechanics #Nonlinear Dynamics and Pattern Formation #Physics #Plasma #Prandtl number #Quantum mechanics #Reynolds number #Rotation (mathematics) #Taylor number #Taylor–Couette flow #Thermodynamics #Toroid #Turbulence #astro-ph
paper · pdf · doi:10.1103/physreve.76.056309
8 pages, 4 figures, submitted to Phys. Rev. E
arxiv created 2006/11/17 · openalex publication_date 2007/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the linear stability of dissipative magnetic Taylor-Couette flow with imposed toroidal magnetic fields. The inner and outer cylinders can be either insulating or conducting; the inner one rotates, the outer one is stationary. The magnetic Prandtl number can be as small as 10(-5) , approaching realistic liquid-metal values. The magnetic field destabilizes the flow, except for radial profiles of B(phi)(R) close to the current-free solution. The profile with B(in)=B(out) (the most uniform field) is considered in detail. For weak fields the Taylor-Couette flow is stabilized, until for moderately strong fields the m=1 azimuthal mode dramatically destabilizes the flow again so that a maximum value for the critical Reynolds number exists. For sufficiently strong fields (as measured by the Hartmann number) the toroidal field is always unstable, even for the nonrotating case with Re=0 . The electric currents needed to generate the required toroidal fields in laboratory experiments are a few kA if liquid sodium is used, somewhat more if gallium is used. Weaker currents are needed for wider gaps, so a wide-gap apparatus could succeed even with gallium. The critical Reynolds numbers are only somewhat larger than the nonmagnetic values; hence such experiments would work with only modest rotation rates.