1109.4442 (Eric Buchlin)
Eric Buchlin
Context: Direct numerical simulations have shown that the dynamo is efficient
even at low Prandtl numbers, i.e., the critical magnetic Reynolds number Rm_c
necessary for the dynamo to be efficient becomes smaller than the hydrodynamic
Reynolds number Re when Re -> infinity. Aims: We test the conjecture (Iskakov
et al. 2007) that Rm_c actually tends to a finite value when Re -> infinity,
and we study the behavior of the dynamo growth factor \gamma\ at very low and
high magnetic Prandtl numbers. Methods: We use local and nonlocal shell-models
of magnetohydrodynamic (MHD) turbulence with parameters covering a much wider
range of Reynolds numbers than direct numerical simulations, but of
astrophysical relevance. Results: We confirm that Rm_c tends to a finite value
when Re -> infinity. The limit for Rm -> infinity of the dynamo growth factor
\gamma\ in the kinematic regime behaves like Re^\beta, and, similarly, the
limit for Re -> infinity of \gamma\ behaves like Rm^{\beta'}, with
\beta=\beta'=0.4. Conclusion: Comparison with a phenomenology based on an
intermittent small-scale turbulent dynamo, together with the differences
between the growth rates in the different local and nonlocal models, indicate a
weak contribution of nonlocal terms to the dynamo effect.
View original:
http://arxiv.org/abs/1109.4442
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