Saturation of a Ponomarenko-type fluid dynamo
type: Item
instance of: scholarly article
zbMATH Open document ID: 1007.76098
publication date: 2002-02-28T00:00:00Z
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 76U05
zbMATH DE Number: 1714359
zbMATH Keywords: saturation
zbMATH Keywords: Ponomarenko dynamo
zbMATH Keywords: supercritical bifurcation
zbMATH Keywords: solid body rotation
zbMATH Keywords: critical magnetic Reynolds number
zbMATH Keywords: dynamo threshold
zbMATH Keywords: Hopf bifurcation
MaRDI profile type: Publication
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author: Angel Nuñez
author: F. Petrelis
author: S. Fauve
title: Saturation of a Ponomarenko-type fluid dynamo
review text: 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].
reviewed by: Iván Abonyi
description: scientific article; zbMATH DE number 1714359