Kinematic dynamo action in spherical Couette flow

Abstract

We investigate numerically kinematic dynamos driven by flow of electrically conducting fluid in the shell between two concentric differentially rotating spheres, a configuration normally referred to as spherical Couette flow. We compare between axisymmetric (2D) and fully three dimensional flows, between low and high global rotation rates, between prograde and retrograde differential rotations, between weak and strong nonlinear inertial forces, between insulating and conducting boundaries, and between two aspect ratios. The main results are as follows. Azimuthally drifting Rossby waves arising from the destabilisation of the Stewartson shear layer are crucial to dynamo action. Differential rotation and helical Rossby waves combine to contribute to the spherical Couette dynamo. At a slow global rotation rate, the direction of differential rotation plays an important role in the dynamo because of different patterns of Rossby waves in prograde and retrograde flows. At a rapid global rotation rate, stronger flow supercriticality (namely the difference between the differential rotation rate of the flow and its critical value for the onset of nonaxisymmetric instability) facilitates the onset of dynamo action. A conducting magnetic boundary condition and a larger aspect ratio both favour dynamo action.

Liquid sodium models of the Earth’s core

“…Such systems are geophysically relevant, having a similar geometry to the Earth's core, especially if they approximately match the innerto-outer core radius ratio of 0.35. While not capturing all aspects of the geodynamo, such systems are relatively simple models of dynamo action, providing a straightforward way to achieve the differential rotation that is a key ingredient of many dynamo mechanisms (see, e.g., Wei et al 2012).…”

“…In the kinematic dynamo, a larger aspect ratio (r o /r i ) and conducting boundary layers favor dynamo action (Wei et al 2012). The similar case of the kinematic dynamo in a full-sphere (i.e., no inner sphere), but with boundary conditions that mimic the tangent cylinder flow of spherical Couette (polar caps that rotate at a different rate from the rest of the spherical boundary), was studied by Schaeffer and Cardin (2006).…”

“…Much work has been done in numerical studies relevant to the observations and experiments described above, including simulations of models of the geodynamo and direct numerical simulations of spherical Couette flow. This includes work on both hydrodynamic and hydromagnetic phenomena in spherical Couette, as well as studies of dynamo action in this and related geometries (see Wei et al (2012) for a good overview, which we follow in the sections below, with updates). We first review hydrodynamic studies of spherical Couette flow, in which no magnetic field is present, before moving on to the magnetized case.…”

“…A discussion of a number of recent results can be found in Chp. 7 of Rüdiger et al (2013) and in Wei et al (2012). For the case of an applied field that is axisymmetric about the rotation axis of the spheres, the fluid is divided into regions magnetically coupled to either one or both of the spheres (see, e.g., Hollerbach and Skinner (2001)).…”

“…By considering the mixed case (overall rotation with an applied field), they showed that these two different cases are smoothly connected. For a useful overview of this work, see also Wei et al (2012). Gissinger et al (2011) investigated instabilities of magnetized spherical Couette flow for a variety of Ro, imposed fields, and magnetic boundary conditions.…”