Saturation of a Ponomarenko-type fluid dynamo (Q2776130)
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scientific article; zbMATH DE number 1714359
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Saturation of a Ponomarenko-type fluid dynamo |
scientific article; zbMATH DE number 1714359 |
Statements
28 February 2002
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saturation
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Ponomarenko dynamo
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supercritical bifurcation
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solid body rotation
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critical magnetic Reynolds number
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dynamo threshold
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Hopf bifurcation
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0.88385206
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0.87587965
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0.8731751
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0.86348283
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0.85805386
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0.85029954
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0.8420884
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0.84152997
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Saturation of a Ponomarenko-type fluid dynamo (English)
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The authors study a relation between solid body rotation ane translation up to dynamo threshold. The configuration found by \textit{Yu. B. Ponomarenko} [J. Appl. Mech. Tech. Phys. 14, 775 ff (1973)] is used a starting point, and the growth of the magnetic field is calculated. The critical magnetic Reynolds number is shown to reach a minimum value. If the magnetic field saturates just above the dynamo threshold, one can expect that after a calculable time delay the magnetic field will grow. Thus the authors arrive at a Hopf bifurcation equation and show that the bifurcation is supercritical as the amplitude of magnetic field saturates. It is noted that the equipartition between kinetic and magnetic energies cannot be achieved.NEWLINENEWLINEFor the entire collection see [Zbl 0973.00055].
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