Modes and instabilities in magnetized spherical Couette flow

Abstract

Several teams have reported peculiar frequency spectra for flows in a spherical shell. To address their origin, we perform numerical simulations of the spherical Couette flow in a dipolar magnetic field, in the configuration of the DT S experiment. The frequency spectra computed from time-series of the induced magnetic field display similar bumpy spectra, where each bump corresponds to a given azimuthal mode number m. The bumps show up at moderate Reynolds number (≃ 2 600) if the time-series are long enough (> 300 rotations of the inner sphere). We present a new method that permits to retrieve the dominant frequencies for individual mode numbers m, and to extract the modal structure of the full non-linear flow. The maps of the energy of the fluctuations and the spatio-temporal evolution of the velocity field suggest that fluctuations originate in the outer boundary layer. The threshold of instability if found at Re c = 1 860. The fluctuations result from two coupled instabilities: high latitude Bödewadt-type boundary layer instability, and secondary non-axisymmetric instability of a centripetal jet forming at the equator of the outer sphere. We explore the variation of the magnetic and kinetic energies with the input parameters, and show that a modified Elsasser number controls their evolution. We can thus compare with experimental determinations of these energies and find a good agreement. Because of the dipolar nature of the imposed magnetic field, the energy of magnetic fluctuations is much larger near the inner sphere, but their origin lies in velocity fluctuations that initiate in the outer boundary layer.

Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment

“…Our code, based on spherical harmonic expansion [15] and finite differences in radius, has already been used to simulate the experiment. We restarted the most turbulent computation of Figueroa et al [12] with a new imposed magnetic field containing the additional non-axisymmetric and non-dipolar terms. This simulation reaches Re = 2πf r 2 o /ν = 2.9 × 10 4 (ν is the kinematic viscosity), Rm = 29 and a magnetostrophic regime close to that of the experiment [8].…”

“…Turbulence is generated by the destabilization of the outer boundary layer, yielding plumes that penetrate inward to regions of stronger magnetic fields. There, the velocity fluctuations are damped, but the associated magnetic fluctuations are stronger [12]. Six snapshots of the fields are saved every five turns.…”

Understanding turbulent free-surface vortex flows using a Taylor-Couette flow analogy

“…54 . Perhaps, free-surface vortices, due to their gravitational inflow and outflow properties (absent in the Taylor-Couette flow) together with secondary flow rotational instabilities, may provide further insight into the behaviour of large meteorological systems 16,54–56 or flows on a grander cosmological scale such as black hole accretion disk dynamics 57 . Jones 58 speculates that the galactic structure may be maintained by an inflow of stars and gas as they fall into the black hole; directly analogous with how a free-surface vortex is maintained 9,10 .…”

Flow instabilities in the wide-gap spherical Couette system

“…In the smaller experiment the inner core is a permanent magnet which at least allows the study of the effect of Lorentz forces. Several numerical studies explore the dynamics and dynamo action in these magnetic spherical Couette systems (Dormy, Cardin & Jault 1998;Schaeffer & Cardin 2006;Hollerbach 2009;Guervilly & Cardin 2010;Cao et al 2012;Wei, Jackson & Hollerbach 2012;Figueroa et al 2013).…”