Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2009-11-23
Phys. Rev. E 81, 036317 (2010)
Nonlinear Sciences
Chaotic Dynamics
9 pages, 9 figures
Scientific paper
10.1103/PhysRevE.81.036317
We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydrodynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number $Pr_{\rm M}$ and the magnetic Reynolds number $Re_{\rm M}$. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium, first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the $(Pr^{-1}_{\rm M}, Re_{\rm M})$ plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.
Mitra Dhrubaditya
Pandit Rahul
Sahoo Ganapati
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