Energy transfers and magnetic energy growth in small-scale dynamo

¹ Department of Physics, Indian Institute of Technology - Kanpur 208016, India
² Mechanical Engineering, Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology - Thuwal 23955-6900, Kingdom of Saudi Arabia

^(a) rohitkr@iitk.ac.in
^(b) mkv@iitk.ac.in
^(c) ravi.samtaney@kaust.edu.sa

Received: 27 July 2013
Accepted: 5 December 2013

Abstract

In this letter we investigate the dynamics of magnetic energy growth in small-scale dynamo by studying energy transfers, mainly energy fluxes and shell-to-shell energy transfers. We perform dynamo simulations for the magnetic Prandtl number on 1024³ grid using the pseudospectral method. We demonstrate that the magnetic energy growth is caused by nonlocal energy transfers from the large-scale or forcing-scale velocity field to small-scale magnetic field. The peak of these energy transfers moves towards lower wave numbers as dynamo evolves, which is the reason why the integral scale of the magnetic field increases with time. The energy transfers U2U (velocity to velocity) and B2B (magnetic to magnetic) are forward and local.