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Nonlinear simulations of magnetic Taylor‐Couette flow with currentfree helical magnetic fields
Author(s) -
Szklarski J.,
Rüdiger G.
Publication year - 2006
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.200610662
Subject(s) - magnetic prandtl number , physics , prandtl number , magnetic field , mechanics , couette flow , magnetohydrodynamics , instability , taylor–couette flow , toroid , reynolds number , nonlinear system , classical mechanics , flow (mathematics) , taylor number , turbulence , nusselt number , heat transfer , plasma , quantum mechanics
Themagnetorotational instability (MRI) in cylindrical Taylor‐Couette flow with external helical magnetic field is simulated for infinite and finite aspect ratios. We solve the MHD equations in their small Prandtl number limit and confirm with timedependent nonlinear simulations that the additional toroidal component of the magnetic field reduces the critical Reynolds number from O (10 6 ) (axial field only) to O (10 3 ) for liquid metals with their small magnetic Prandtl number. Computing the saturated state we obtain velocity amplitudes which help designing proper experimental setups. Experiments with liquid gallium require axial field ∼50 Gauss and axial current ∼4 kA for the toroidal field. It is sufficient that the vertical velocity u z of the flow can be measured with a precision of 0.1 mm/s.We also show that the endplates enclosing the cylinders do not destroy the traveling wave instability which can be observed as presented in earlier studies. For TC containers without and with endplates the angular momentum transport of the MRI instability is shown as to be outwards. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)