Generalised quasi-linear approximation of the HMRI

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).

arXiv comment17 pages, 8 figures

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Cited by in corpus (10)

• The Generalized Quasilinear Approximation: Application to Zonal Jets
• Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence
• Three-Dimensional Rotating Couette Flow Via The Generalised Quasilinear Approximation
• Exploiting self-organized criticality in strongly stratified turbulence
• Generalised quasilinear approximations of turbulent channel flow: Part 2. Spanwise scale interactions
• Direct Statistical Simulation of Jets and Vortices in 2D Flows
• Joint Instability and Abrupt Nonlinear Transitions in a Differentially Rotating Plasma
• Generalised Quasilinear Approximation of the Interaction of Convection and Mean Flows in a Thermal Annulus
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow
• Direct Statistical Simulation Using Generalised Cumulant Expansions