Generalised quasi-linear approximation of the HMRI

TL;DR

This study evaluates the generalized quasi-linear approximation (GQL) in simulating the helical magnetorotational instability (HMRI), demonstrating GQL's superior accuracy over traditional quasilinear methods in capturing key statistical features.

Contribution

The paper introduces and tests the GQL approximation for HMRI, showing it improves statistical accuracy over QL by including large-scale mode interactions.

Findings

GQL outperforms QL in statistical descriptions of HMRI.

GQL remains effective with few large-scale modes.

GCE2 based on GQL is more accurate than CE2 based on QL.

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).