Applied Maths Seminar: Hollerbach -- Magnetorotational Instabilities in Cylindrical Taylor-Couette Flow

Rainer Hollerbach, Department of Applied Mathematics, University of Leeds 

Taylor-Couette flow, the flow between differentially rotating cylinders, is one of the
oldest problems in classical fluid dynamics, but still continues to attract considerable
attention to this day.  Now suppose the fluid is taken to be electrically conducting,
and a magnetic field is applied.  Magnetohydrodynamic effects then arise, which can
yield fundamentally new results that have no analog in the nonmagnetic problem.  The
magnetorotational instability (MRI) is one such result, whereby magnetic effects
destabilize an otherwise stable flow.  In this talk I will begin by discussing the
physics underlying the MRI, as well as it astrophysical significance.  I will next
reduce the governing equations to a linear eigenvalue problem, and show how the geometry
of the externally imposed magnetic field, whether it is purely axial or also contains an
azimuthal component, makes an enormous difference to the solutions.  Finally, I will
present a series of experimental results on the MRI in such mixed axial+azimuthal
magnetic fields, and compare them with the theoretical predictions