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arXiv · 1510.00122

Dynamos at extreme magnetic Prandtl numbers: Insights from shell models

Mahendra K. Verma·Rohit Kumar
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Abstract

We present an MHD shell model suitable for computation of various energy fluxes of magnetohydrodynamic turbulence for very small and very large magnetic Prandtl numbers $\mathrm{Pm}$; such computations are inaccessible to direct numerical simulations. For small $\mathrm{Pm}$, we observe that both kinetic and magnetic energy spectra scale as $k^{-5/3}$ in the inertial range, but the dissipative magnetic energy scales as $k^{-11/3}\exp(-k/k_η)$. Here, the kinetic energy at large length scale feeds the large-scale magnetic field that cascades to small-scale magnetic field, which gets dissipated by Joule heating. The large-$\mathrm{Pm}$ dynamo has a similar behaviour except that the dissipative kinetic energy scales as $k^{-13/3}$. For this case, the large-scale velocity field transfers energy to the large-scale magnetic field, which gets transferred to small-scale velocity and magnetic fields; the energy of the small-scale magnetic field also gets transferred to the small-scale velocity field, and the energy thus accumulated is dissipated by the viscous force.

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Mahendra K. Verma, Rohit Kumar. 2016-09-20. Dynamos at extreme magnetic Prandtl numbers: Insights from shell models. https://doi.org/10.1080/14685248.2016.1228937

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