Effects of Global Rotation on the Mean-Field Magnetohydrodynamics of the Derviche Tourneur Sodium (DTS) Experiment

Abstract:

Magnetic fields are ubiquitous in the observed universe. Stars and planets,
including our own, have self-induced, dynamic magnetic fields generated and
modified by the interplay between these fields and the conductive fluids within
the astrophysical bodies. The generation step is a particular problem, as a
2-dimensional flow can amplify an existing magnetic field (e.g. through field line
stretching by sheared flow, a.k.a. the Ω effect), but cannot create the observed
dipole field without an additional mechanism (such as field line twisting by
helical eddies, a.k.a the α effect). Laboratory astrophysics in general, and the
DTS experiment in particular, seek to aid understanding of these dynamics.

DTS consists of a spherical Couette flow (two spheres, on inside the other,
in co- or counter-rotation) with a permanent dipole magnetic field originating in
the inner sphere. Previous campaigns, with a stationary outer sphere, demonstrated
an anomalous induced magnetic field best modeled by a turbulent magnetic
diffusivity (β effect) that was negative in the bulk of the flow and positive
near the outer edge, a result not present in the associated direct numerical
simulations (DNS). We present data from a new campaign (both numerical
and experimental, though we focus on the numerical here) with a rotating
outer sphere, which aims to demonstrate the persistence (or lack thereof) of
the negative β effect under global rotation.

The forward modeling of the kinematic induction problem finds the magnetic
field profile generated by a specified axisymmetric flow, as well as specified α
and β profiles. From this profile it is easy to generate simulated data which
can be compared to experimental or DNS results. Standard nonlinear inversion
techniques are then used to find the best fitting model.