Ponomarenko dynamo with time-periodic flow

The Ponomarenko dynamo theory is revisited to take into account time-dependent flows. Our purpose is to investigate how a small departure from a steady flow can modify the onset of dynamo action. We consider a typical helical flow when the velocity components are modulated in time at the same freque...

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Bibliographic Details
Published in:Physics of fluids (1994) 2003-06, Vol.15 (6), p.1606-1611
Main Author: Normand, Christiane
Format: Article
Language:English
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Summary:The Ponomarenko dynamo theory is revisited to take into account time-dependent flows. Our purpose is to investigate how a small departure from a steady flow can modify the onset of dynamo action. We consider a typical helical flow when the velocity components are modulated in time at the same frequency and with a small modulation amplitude of the order ε. Using ε as an expansion parameter we calculated the shift in the critical magnetic Reynolds number and the shift in frequency at dynamo onset. We found that modulation can either lower or enhance the threshold of dynamo action depending on ε 1 , the relative amplitude of modulation of the azimuthal and axial velocity components. More specifically, in-phase modulation with 0.7⩽ε 1 ⩽1 delays the onset of dynamo action, while in a larger range including out-of-phase modulation, −1⩽ε 1
ISSN:1070-6631
1089-7666
DOI:10.1063/1.1571547