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Comparison of forcing functions in magnetohydrodynamics

Mairi E. McKay1,*, Moritz Linkmann2, Daniel Clark1, Adam A. Chalupa1, and Arjun Berera1,†

  • 1The School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
  • 2Department of Physics & INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy

  • *mairi.mckay@ed.ac.uk
  • †ab@ph.ed.ac.uk
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Phys. Rev. Fluids 2, 114604 – Published 13 November, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.114604

Abstract

Results are presented of direct numerical simulations of incompressible, homogeneous magnetohydrodynamic turbulence without a mean magnetic field, subject to different mechanical forcing functions commonly used in the literature. Specifically, the forces are negative damping (which uses the large-scale velocity field as a forcing function), a nonhelical random force, and a nonhelical static sinusoidal force (analogous to helical ABC forcing). The time evolution of the three ideal invariants (energy, magnetic helicity, and cross helicity), the time-averaged energy spectra, the energy ratios, and the dissipation ratios are examined. All three forcing functions produce qualitatively similar steady states with regard to the time evolution of the energy and magnetic helicity. However, differences in the cross-helicity evolution are observed, particularly in the case of the static sinusoidal method of energy injection. Indeed, an ensemble of sinusoidally forced simulations with identical parameters shows significant variations in the cross helicity over long time periods, casting some doubt on the validity of the principle of ergodicity in systems in which the injection of helicity cannot be controlled. Cross helicity can unexpectedly enter the system through the forcing function and must be carefully monitored.

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Phys. Rev. Fluids 2, 114604– Published 13 November, 2017
  • Received 15 April 2017

©2017 American Physical Society

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