Assessment of a new sub-grid model for magnetohydrodynamical turbulence. II. Kelvin-Helmholtz instability

TL;DR

This paper evaluates a new sub-grid model, MInIT, for magnetohydrodynamical turbulence, specifically applied to Kelvin-Helmholtz instability, demonstrating its ability to predict turbulent stresses accurately in astrophysical simulations.

Contribution

The paper extends the MInIT sub-grid model to Kelvin-Helmholtz instability, providing a new approach to simulate turbulence in magnetized astrophysical systems.

Findings

MInIT accurately predicts turbulent stresses during KHI.

The model's coefficients are calibrated with high-resolution simulations.

Order-of-magnitude agreement with resolved turbulence dynamics.

Abstract

The modelling of astrophysical systems such as binary neutron star mergers or the formation of magnetars from the collapse of massive stars involves the numerical evolution of magnetised fluids at extremely large Reynolds numbers. This is a major challenge for (unresolved) direct numerical simulations which may struggle to resolve highly dynamical features as, e.g. turbulence, magnetic field amplification, or the transport of angular momentum. Sub-grid models offer a means to overcome those difficulties. In a recent paper we presented MInIT, an MHD-instability-induced-turbulence mean-field, sub-grid model based on the modelling of the turbulent (Maxwell, Reynolds, and Faraday) stress tensors. While in our previous work MInIT was assessed within the framework of the magnetorotational instability, in this paper we further evaluate the model in the context of the Kelvin-Helmholtz instability (KHI). The main difference with other sub-grid models (as e.g. the alpha-viscosity model or the gradient model) is that in MInIT we track independently the turbulent energy density at sub-grid scales, which is used, via a simple closure relation, to compute the different turbulent stresses relevant for the dynamics. The free coefficients of the model are calibrated using well resolved box simulations of magnetic turbulence generated by the KHI. We test the model against these simulations and show that it yields order-of-magnitude accurate predictions for the evolution of the turbulent Reynolds and Maxwell stresses.