Saas-Fee 2009: Solar and Stellar Dynamos – Supplementary material

This Web page contains links to animation complementing the set of class notes I wrote for the 39th Saas-Fee Advanced Course, held in Les Diablerets, Switzerland, from 2009 March 23 to 28. Animations are organized by section numbers in the class notes. All are in mpeg format.

Paul Charbonneau, 
Département de physique 
Université de Montréal

2.3 Magnetic field evolution in a cellular flow

2.3.1 A cellular flow solution

This is an animated version of Figure 2.7. Magnetic fieldlines are superposed onto a color scale encoding the magnitude of the magnetic field. Green dots are Lagrangian tracers, i.e., floating corks passively advected by the flow. This solutions has a magnetic Reynolds number Rm=1000, and time is measured in units of the turnover time L/U; a full revolution on the “fastest” streamline requires a time t/pi=0.532.

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2.3.3 The electromagnetic skin depth

This is an animation of an oscillating magnetic field diffusing into an electrical conductor, and illustrating the notion opf electromagnetic skin depth. Time is measured in units of the boundary oscillation period. The solution (yellow line) is for omega=1 and eta=0.1. The two green curves illustrate the exponential envelope multiplying the purely oscillating component, and the blue vertical line segments indicate the extent of the electromagnetic skin depth, as given by equation (2.37), measured from y=0.

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2.3.4 Timescales for field amplification and decay

Similar to above solution (Rm=1000), but now with periodic boundary conditions, and the solution is followed for 5 turnover times.

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The following solutions is identical except for the initial condition, now chosen such that the value of the vector potential A averaged over each flow streamline is now different from one streamline to the next. The solution is now followed over 20 turnover times. Dissipation of the magnetic field now takes place in three more or less distinct phases, as described in the notes. Notice how, in the final “slow” dissipation phase (t/pi=3-300), fieldlines are aligned with the streamlines (as traced by the green floaters).

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2.3.5 Flux expulsion in spherical geometry: axisymmetrization

These two animations illustrate the axisymmetrization process by axisymmetric differential rotation of a dipolar magnetic field whose symmetry axis is inclined with respect to the rotational axis. Color contours map the evolving surface distribution of the radial magnetic field component: yellow to green for positive Br, and cyan to blue for negative values. The polarity inversion line (Br=0 is drawn with as thicker contour. In both cases the viewpoint is looking straight down at a latitude of 60 degrees.

The first animation is for a dipole inclined by 60 degrees, (as on Figure 2.10), and the second for a perpendicular dipole (90 degrees inclination). Note how in the latter case the field is completely dissipated.

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2.5 The CP flow and fast dynamo action

2.5.1 Dynamo action at last

These two animations illustrate the spatiotemporal evolution of the z-component of the magnetic field (perpendicular to the image plane), for the CP flow at Rm=100 and Rm=1000. Color scale as on Figure 2.12, and the green lines indicate the location of cell separatrix surfaces. Time is measured in units of the turnover time.

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3.2 Mean-field dynamo models

3.2.8 Linear alpha-Omega dynamo solutions

The left animation is an animated version of Figure 3.4; the animation on the right uses a negative dynamo number but is otherwise identical.

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3.2.11 alpha-Omega models with meridional circulation

This is an animated version of Figure 3.7, see Figure caption and accompanying text for details.

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3.3 Babcock-Leighton models

3.3.1 Sunspot decay and the Babcock-Leighton mechanism

This is an animated version of Figure 3.10, see Figure caption and accompanying text for details.

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3.3.5 A sample solution

This is an animated version of Figure 3.13, see Figure caption and accompanying text for details.

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3.5 Global MHD simulations

**** UNDER CONSTRUCTION **** These are [will be] animated versions of Figure 3.17, see Figure caption and accompanying text for details on the color-coding scheme. The animations of the subsurface radial velocity and magnetic field components span only 10 solar days, to properly show the character of MHD convection, while the animation for the zonally-averaged toroidal magnetic component at the base of the convective envelope covers a much longer time span at much lower temporal cadence, in order to show a few polarity reversals.

-Last Revised 1 February 2010 by

Added on SSAA website March 26, 2020 by SSAA webmaster.