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Generalised quasilinear approximation of the helical magnetorotational instability

Part of: Focus on Plasma Astrophysics

Published online by Cambridge University Press:  13 May 2016

Adam Child ,
Rainer Hollerbach ,
Brad Marston  and
Steven Tobias
Adam Child*
Affiliation:
Department of Mathematics, University of Leeds, Leeds, LS2 9JT, UK
Rainer Hollerbach
Affiliation:
Department of Mathematics, University of Leeds, Leeds, LS2 9JT, UK
Brad Marston
Affiliation:
Department of Physics, Brown University, Box 1843, Providence, RI 02912, USA
Steven Tobias
Affiliation:
Department of Mathematics, University of Leeds, Leeds, LS2 9JT, UK
*
†Email address for correspondence: [email protected]
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Abstract

Motivated by recent advances in direct statistical simulation (DSS) of astrophysical phenomena such as out-of-equilibrium jets, we perform a direct numerical simulation (DNS) of the helical magnetorotational instability (HMRI) under the generalised quasilinear approximation (GQL). This approximation generalises the quasilinear approximation (QL) to include the self-consistent interaction of large-scale modes, interpolating between fully nonlinear DNS and QL DNS whilst still remaining formally linear in the small scales. In this paper we address whether GQL can more accurately describe low-order statistics of axisymmetric HMRI when compared with QL by performing DNS under various degrees of GQL approximation. We utilise various diagnostics, such as energy spectra in addition to first and second cumulants, for calculations performed for a range of Reynolds and Hartmann numbers (describing rotation and imposed magnetic field strength respectively). We find that GQL performs significantly better than QL in describing the statistics of the HMRI even when relatively few large-scale modes are kept in the formalism. We conclude that DSS based on GQL (GCE2) will be significantly more accurate than that based on QL (CE2).

Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 3 , June 2016 , 905820302
Copyright
© Cambridge University Press 2016 

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