2003/08/31 by A. A. Schekochihin, S. C. Cowley, J. L. Maron +3 · 3 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Geomagnetism and Paleomagnetism Studies #Magnetic and Electromagnetic Effects #Solar and Space Plasma Dynamics #astro-ph #nlin.CD #physics.flu-dyn #physics.geo-ph
paper · pdf · doi:10.1103/physrevlett.92.054502
published as Phys.Rev.Lett.92:054502,2004 · revtex, 4 pages, 5 figures; minor changes to match published version
openalex publication_date 2004/02/03 · arxiv created 2004/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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\ensuremath\lesssim1 even for Rm for which dynamo exists at Prm\ensuremath≥1. We argue that, in the limit of Re\ensuremath→\ensuremath∞, a finite Prm,c may exist. The second possibility is that Prm,c\ensuremath→0 as Re\ensuremath→\ensuremath∞, 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\ensuremath\gtrsim220 for Prm\ensuremath≤1/8. This is larger than Rm in many planets and in all liquid-metal experiments.