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Magnetohydrodynamic activity inside a sphere
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10.1063/1.2393438
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Affiliations:
1 National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colorado 80307
2 Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755
Phys. Fluids 18, 116602 (2006)
/content/aip/journal/pof2/18/11/10.1063/1.2393438
http://aip.metastore.ingenta.com/content/aip/journal/pof2/18/11/10.1063/1.2393438
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## Figures

FIG. 1.

Speed-up of the code in two Linux clusters in parallel simulations with . The dotted line indicates the ideal scaling.

FIG. 2.

Total energy (dotted line), magnetic energy (solid line), and kinetic energy (dashed line) as a function of time in run II. At late times the system is dominated by magnetic energy. Since the only dynamic evolution possible for requires a velocity and since the kinetic energy has essentially disappeared, the system has “frozen” into a nearly purely magnetic state, which can only slowly resistively decay hereafter.

FIG. 3.

Relative magnetic helicity as a function of time for runs I (solid line) and II (dashed line). The relative helicity at late times increases with the Reynolds number. Note the maximum possible value for the relative helicity is .

FIG. 4.

Spectrum of kinetic energy as a function of for run II, at (solid line), (dotted line), and (dashed line). Note the appearance of a clear dissipation range.

FIG. 5.

Spectrum of magnetic energy as a function of for run II, at (solid line), (dotted line), and (dashed line). A magnetic dissipation range becomes clearly visible.

FIG. 6.

Amplitude of the coefficients in run II at as a function of and (summed over all values of ). Most of the magnetic energy is at the largest available scale, and an asymmetry is observed between positive and negative values of .

FIG. 7.

(Color online) Above: kinetic energy density and velocity field lines in run II, at (left) and at (right). Below: magnetic energy density and magnetic field lines in the same run, at (left) and at (right). For convenience, intensity and field lines are always shown in pairs, with intensity on the left and field lines on the right.

FIG. 8.

(Color online) Intensity of the forcing function used in the dynamo simulations (left), and associated field lines (right). Above: function used in run III. Below: function used in runs IV and V.

FIG. 9.

Kinetic (dashed line) and magnetic energy (solid line) as a function of time in run III.

FIG. 10.

Trace of the magnetic dipole orientation on the unit sphere (above) and magnitude of the dipole moment as a function of time (below) in run III.

FIG. 11.

(Color online) Above: kinetic energy density and velocity field lines in run III, at . Below: magnetic energy density and magnetic field at the same time. The same conventions as in Fig. 7 are used.

FIG. 12.

Kinetic (dashed line) and magnetic energy (solid line) as a function of time in run IV.

FIG. 13.

Trace of the magnetic dipole orientation on the unit sphere (above) and magnitude of the dipole moment as a function of time (below) in run IV.

FIG. 14.

(Color online) Kinetic energy spectrum at [thick (blue) solid line] and at [thick (blue) dashed-dotted line] in run IV; the thin lines correspond to the magnetic energy spectrum at (solid), (dotted), (dashed), and (dashed-dotted).

FIG. 15.

(Color online) Above: kinetic energy density and velocity field lines in run IV, at (left) and at (right). Below: magnetic energy density and magnetic field lines in the same run, at (left) and at (right). The same conventions than in Fig. 7 are used.

FIG. 16.

Kinetic (dashed line) and magnetic energy (solid line) as a function of time in run V.

FIG. 17.

Time evolution of the three components of the dipole moment in run V. Labels are as in Fig. 10.

FIG. 18.

(Color online) Kinetic energy spectrum at [thick (blue) solid line] and at [thick (blue) dash-triple dotted line] in run V; the thin lines correspond to the magnetic energy spectrum at (solid), (dotted), (dashed), (dashed-dotted), and (dashed-triple dotted).

FIG. 19.

(Color online) Above: kinetic energy density and velocity field lines in run V, at (left) and at (right). Below: magnetic energy density and magnetic field lines in the same run, at (left) and at (right). We were unable to find an ordered pattern in either field.

/content/aip/journal/pof2/18/11/10.1063/1.2393438
2006-11-30
2014-04-20

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