Physics – Fluid Dynamics
Scientific paper
2007-01-12
Physics
Fluid Dynamics
19 pages, 9 figures, published in the Journal of Turbulence
Scientific paper
We investigate the dynamo problem in the limit of small magnetic Prandtl number ($\Pm$) using a shell model of magnetohydrodynamic turbulence. The model is designed to satisfy conservation laws of total energy, cross helicity and magnetic helicity in the limit of inviscid fluid and null magnetic diffusivity. The forcing is chosen to have a constant injection rate of energy and no injection of kinetic helicity nor cross helicity. We find that the value of the critical magnetic Reynolds number ($\Rm$) saturates in the limit of small $\Pm$. Above the dynamo threshold we study the saturated regime versus $\Rm$ and $\Pm$. In the case of equipartition, we find Kolmogorov spectra for both kinetic and magnetic energy except for wave numbers just below the resistive scale. Finally the ratio of both dissipation scales (viscous to resistive) evolves as $\Pm^{-3/4}$ for $\Pm < 1$
Plunian Franck
Stepanov Rodion
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