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Numerical study of dynamo action at low magnetic Prandtl numbers

Y. Ponty·P. D. Mininni·D. C. Montgomery·J. -F. Pinton·H. Politano·A. Pouquet
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Abstract

We present a three--pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers $P_M$. The difficulty of resolving a large range of scales is circumvented by combining Direct Numerical Simulations, a Lagrangian-averaged model, and Large-Eddy Simulations (LES). The flow is generated by the Taylor-Green forcing; it combines a well defined structure at large scales and turbulent fluctuations at small scales. Our main findings are: (i) dynamos are observed from $P_M=1$ down to $P_M=10^{-2}$; (ii) the critical magnetic Reynolds number increases sharply with $P_M^{-1}$ as turbulence sets in and then saturates; (iii) in the linear growth phase, the most unstable magnetic modes move to small scales as $P_M$ is decreased and a Kazantsev $k^{3/2}$ spectrum develops; then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.

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BibTeXRIS

Y. Ponty, P. D. Mininni, D. C. Montgomery, J. -F. Pinton, H. Politano, A. Pouquet. 2004-10-07. Numerical study of dynamo action at low magnetic Prandtl numbers. https://doi.org/10.1103/physrevlett.94.164502

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