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Insufficient numerical resolution of grid-based, direct numerical simulations(DNS) hampers the development of instabilitydriven turbulence at small(unresolved) scales. As an alternative to DNS, sub-grid models can potentiallyreproduce the effects of turbulence at small scales in terms of the resolvedscales, and hence can capture physical effects with less computationalresources. We present a new sub-grid model, theMHD-instability-induced-turbulence (MInIT) mean-field model. MInIT is aphysically motivated model based on the evolution of the turbulent (Maxwell,Reynolds, and Faraday) stress tensors and their relation with the turbulentenergy densities of the magneto-rotational (MRI) and parasitic instabilities,modeled with two partial differential evolution equations with stiff sourceterms. Their solution allows obtaining the turbulent stress tensors through theconstant coefficients that link them to the energy densities. The model isassessed using data from MRI in-box DNS and applying a filtering operation tocompare the filtered data with that from the model. Using the $L_2$-norm as themetric for the comparison, we find less than one order-of-magnitude differencebetween the two sets of data. No dependence on filter size or length scale ofunresolved 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 ofthe stresses increases with filter size. We conclude that MInIT can help DNS byproperly capturing small-scale turbulent stresses which has potentialimplications on the dynamics of highly-magnetized rotating compact objects,such as those formed during binary neutron star mergers.

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