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University of Sydney
School of Mathematics and Statistics
Dr David Ivers
School of Mathematics and Statistics, University of Sydney
Time-Stepping Dynamical Dynamos in Spherical Geometries
Wednesday, 29th May, 2-3pm, Carslaw 173.
The main magnetic fields of the larger planets, the Earth, possibly
Mercury and the Sun are generated by the motions in
electrically-conducting cores or shells. Motions which are sufficiently
vigorous and asymmetric can act as self-exciting dynamos. Attempts are
also underway by several research groups to develop laboratory rotating
fluid dynamos. I will talk about pseudo-spectral dynamo codes, which I
have been developing as a computational laboratory for the study of such
dynamos. The prototype model underlying the codes incorporates the
dynamics of an electrically-conducting rotating liquid spherical shell
surrounded by a stationary electrically-insulating mantle and enclosing
a solid inner core. The Boussinesq approximation is made, in which
density variations are retained only in the buoyancy force. The
convection is thermally driven by prescribed temperatures at the inner
and outer core boundaries. The magnetic field, the velocity, the
pressure and the temperature in the shell are governed by the magnetic
induction equation, the heat equation and the Navier-Stokes momentum
equation in a uniformly rapidly rotating reference frame with inertia,
including the non-linear advective term, Coriolis, buoyancy, viscous and
magnetic Lorentz forces. The magnetic field and the velocity are
solenoidal. The magnetic, viscous and thermal diffusivities are
uniform.
Results are presented for three benchmark models: non-magnetic thermal
convection with a non-rotating inner-core; a convective dynamo with a
non-rotating electrically-insulating inner-core; and a convective dynamo
with a rotating electrically-conducting inner core, which can rotate
freely about rotation axis of the mantle under the control of the axial
viscous and magnetic torques at the inner-core boundary.
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