Dynamos at extreme magnetic Prandtl numbers: insights from shell models. Issue 12 (1st December 2016)

• Record Type: Journal Article
• Authors: Verma, Mahendra K.; Kumar, Rohit
• Is Part Of: Journal of turbulence. Volume 17:Issue 12(2016)
• Page Start: 1112
• Page End: 1141
• Publication Date: 2016-12-01
• Subjects: Magnetic field generation -- dynamo -- energy transfers -- shell model -- magnetohydrodynamic turbulence; Turbulence -- Periodicals; Turbulence -- Périodiques; 532.0527
• DOI: 10.1080/14685248.2016.1228937
• Languages: English
• ISSNs: 1468-5248

Abstract

ABSTRACT: We present a magnetohydrodynamic (MHD) shell model suitable for computation of various energy fluxes of MHD turbulence for very small and very large magnetic Prandtl numbers Pm; such computations are inaccessible to direct numerical simulations. For small 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-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.