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Title:
Critical Magnetic Prandtl Number for Small-Scale Dynamo
Authors:
Schekochihin, Alexander A.; Cowley, Steven C.; Maron, Jason L.; McWilliams, James C.
Affiliation:
AA(Plasma Physics Group, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2BW, United Kingdom), AB(Plasma Physics Group, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2BW, United Kingdom), AC(Plasma Physics Group, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2BW, United Kingdom), AD(Plasma Physics Group, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2BW, United Kingdom)
Publication:
Physical Review Letters, vol. 92, Issue 5, id. 054502 (PhRvL Homepage)
Publication Date:
02/2004
Origin:
APS
PACS Keywords:
Isotropic turbulence, homogeneous turbulence, Origins and models of the magnetic field, dynamo theories, Magnetohydrodynamics and plasmas
DOI:
10.1103/PhysRevLett.92.054502
Bibliographic Code:
2004PhRvL..92e4502S

Abstract

We report a series of numerical simulations showing that the critical magnetic Reynolds number Rmc for the nonhelical small-scale dynamo depends on the Reynolds number Re. Namely, the dynamo is shut down if the magnetic Prandtl number Prm=Rm/Re is less than some critical value Prm,c≲1 even for Rm for which dynamo exists at Prm≥1. We argue that, in the limit of Re→∞, a finite Prm,c may exist. The second possibility is that Prm,c→0 as Re→∞, while Rmc tends to a very large constant value inaccessible at current resolutions. If there is a finite Prm,c, the dynamo is sustainable only if magnetic fields can exist at scales smaller than the flow scale, i.e., it is always effectively a large-Prm dynamo. If there is a finite Rmc, our results provide a lower bound: Rmc≳220 for Prm≤1/8. This is larger than Rm in many planets and in all liquid-metal experiments.
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