Alexander Schekochihin ,   University of Cambridge

  
We report a series of numerical simulations showing that the critical magnetic Reynolds number Rm_c
for the nonhelical small-scale dynamo depends on the Reynolds number Re.
Namely, the dynamo is shut down if the magnetic Prandtl number Pm=Rm/Re is less than some critical value Pm_c
even for Rm for which dynamo exists at Pm>1. We argue that, in the limit of Re->infinity, a finite Pm_c may exist.
The second possibility is that Pm_c->0 as Re->infinity, while Rm_c
tends to a very large constant value inaccessible at current resolutions.
If there is a finite Pm_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-Pm dynamo.
If there is a finite Rm_c, our results provide a lower bound: Rm_c>220 for Pm<1/8.
This is larger than Rm in many planets and in all liquid-metal experiments.