4.7 Article

Assessment of a new sub-grid model for magnetohydrodynamical turbulence. I. Magnetorotational instability

Journal

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Volume 517, Issue 3, Pages 3505-3524

Publisher

OXFORD UNIV PRESS
DOI: 10.1093/mnras/stac2888

Keywords

instabilities; (magnetohydrodynamics) MHD; turbulence; methods: numerical

Funding

  1. Spanish Agencia Estatal de Investigacion [PGC2018-095984-B-I00, PID2021-125485NB-C21, PID2021-127495NB-I00]
  2. Generalitat Valenciana [PROMETEO/2019/071]
  3. Ministerio de Universidades de Espana (Spanish Ministry of Universities) through the Ayuda para la Formacion de Profesorado Universitario (FPU) [FPU19/01750]
  4. Spanish Ministry of Science, Innovation and Universities via the Ramon y Cajal programme [RYC2018-024938-I]

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In this study, a new sub-grid model called MInIT mean-field model is proposed to capture the effects of turbulence at small scales. Through linking the turbulent stress tensors with the energy densities, the model successfully simulates the DNS data of MRI in-box and compares it with the filtered data.
Insufficient numerical resolution of grid-based, direct numerical simulations (DNS) hampers the development of instability-driven turbulence at small (unresolved) scales. As an alternative to DNS, sub-grid models can potentially reproduce the effects of turbulence at small scales in terms of the resolved scales, and hence can capture physical effects with less computational resources. We present a new sub-grid model, the MHD-instability-induced-turbulence (MInIT) mean-field model. MInIT is a physically motivated model based on the evolution of the turbulent (Maxwell, Reynolds, and Faraday) stress tensors and their relation with the turbulent energy densities of the magnetorotational (MRI) and parasitic instabilities, modelled with two partial differential evolution equations with stiff source terms. Their solution allows obtaining the turbulent stress tensors through the constant coefficients that link them to the energy densities. The model is assessed using data from MRI in-box DNS and applying a filtering operation to compare the filtered data with that from the model. Using the L-2-norm as the metric for the comparison, we find less than one order-of-magnitude difference between the two sets of data. No dependence on filter size or length scale of unresolved scales is found, as opposed to results using the gradient model (which we also use to contrast our model) in which the L-2-norm of some of the stresses increases with filter size. We conclude that MInIT can help DNS by properly capturing small-scale turbulent stresses which has potential implications on the dynamics of highly magnetized rotating compact objects, such as those formed during binary neutron star mergers.

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