Hydromagnetic Taylor--Couette flow: numerical formulation and comparison with experiment

Abstract

Taylor--Couette flow in the presence of a magnetic field is a problem belonging to classical hydromagnetics and deserves to be more widely studied than it has been to date. In the nonlinear regime the literature is scarce. We develop a formulation suitable for solution of the full three dimensional nonlinear hydromagnetic equations in cylindrical geometry, which is motived by the formulation for the magnetic field. It is suitable for study at finite magnetic Prandtl numbers and in the small Prandtl number limit, relevant to laboratory liquid metals. The method is used to determine the onset of axisymmetric Taylor vortices, and finite amplitude solutions. Our results compare well with existing linear and nonlinear hydrodynamic calculations and with hydromagnetic experiments.

14 pages, 2 figures

References in corpus (3)

• Magnetic Field Saturation in the Riga Dynamo Experiment
• MHD instability in differentially rotating cylindric flows
• Magnetic instability in a sheared azimuthal flow

Cited by in corpus (8)

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• Poloidal-toroidal decomposition in a finite cylinder. I. Influence matrices for the magnetohydrodynamic equations
• The weakly nonlinear magnetorotational instability in a global, cylindrical Taylor-Couette flow
• Hydromagnetic Taylor--Couette flow: wavy modes
• High-speed shear driven dynamos. Part 2. Numerical analysis
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow