Numerical Study of Dynamo Action at Low Magnetic Prandtl Numbers

Creators: Ponty, Yannick; Mininni, P. D.; Montgomery; Pinton, Jean-François; Politano, Helene; Pouquet, Annick

Others:: Laboratoire de Cosmologie, Astrophysique Stellaire & Solaire, de Planétologie et de Mécanique des Fluides (CASSIOPEE) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS); National Center for Atmospheric Research [Boulder] (NCAR); Department of Physics and Astronomy [Hanover] ; Dartmouth College [Hanover]; Laboratoire de Physique de l'ENS Lyon (Phys-ENS) ; École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL) ; Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS); We thank D. Holm for discussions about the model and H. Tufo for providing computer time at UC-Boulder, NSF ARI Grant No. CDA-9601817. NSF Grants No. ATM- 0327533 (Dartmouth) and No. CMG-0327888 (NCAR) are acknowledged. J. F. P., H. P., and Y. P. thank CNRS Dynamo GdR, INSU/PNST, and PCMI Programs for sup- port. Computer time was provided by NCAR, PSC, UC, NERSC, and IDRIS (CNRS).

Description

We present a three-pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers PM. The difficulty of resolving a large range of scales is circumvented by combining direct numerical simulations, a Lagrangian-averaged model and large-eddy simulations. 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 PM=1 down to PM=10^-2, (ii) the critical magnetic Reynolds number increases sharply with P_M^-1 as turbulence sets in and then it saturates, and (iii) in the linear growth phase, unstable magnetic modes move to smaller scales as PM is decreased. Then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.

Numerical Study of Dynamo Action at Low Magnetic Prandtl Numbers

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