[M2 Internship] Magnetorotational instability in an accretion disk

Date : printemps 2027

Abstract

The aim of the project is to investigate the physical mechanisms and processes governing instabilities in an
accretion disc orbiting a massive central object, which may give rise to turbulence. Because pure hydrodynamic
models fail to explain astrophysical data, additional phenomena should be considered in order to explain how
turbulence drives the transport of angular momentum. A primary candidate is the magnetorotational instability
(MRI), which is triggered by the interaction of the accretion disk’s motion with a background magnetic field. The
proposed work will combine numerical simulations within an idealized framework known as the ‘Taylor-Couette
configuration’ with magnetohydrodynamic theory. The results will enable a comparison with the forthcoming
DRESDYN-MRI experiment using liquid sodium, currently under construction at the Helmholtz-Zentrum
Dresden-Rossendorf (HZDR, Germany), which aims to detect and study different types of MRI in the laboratory

Methodology, tools

Numerical computations will be carried out using a fully nonlinear
3D code called SFEMaNS [2], coupled with a linear toolkit enabling the calculation of the most unstable
modes responsible for the instability [3]. Validation will be assessed by comparison with published reference
results.

Benefits, expected results, supervision

The results will be discussed in collaboration with colleagues working
on the development of the future DRESDYN-MRI experiment [1], which uses liquid sodium at the Helmholtz-
Zentrum Dresden-Rossendorf (HZDR). The intern will work with Caroline Nore (head of the fluid mechanics
department at LISN) and Victor Botez, a PhD student. Both are members of the COMET team.

Prerequisites

A background in physics, computer science or physical sciences is required.

Bibliography

[1] F. Stefani, A. Gailitis, G. Gerbeth, A. Giesecke, T. Gundrum, G. Rüdiger, M. Seilmayer, and T. Vogt,
The DRESDYN project: Liquid metal experiments on dynamo action and magnetorotational instability,
Geophys. Astrophys. Fluid Dyn. 113, 51 (2019).
[2] J. L. Guermond, R. Laguerre, J. Léorat et C. Nore : Nonlinear magnetohydrodynamics in axisymmetric
heterogeneous domains using a Fourier/finite element technique and an interior penalty method, J. Comp.
Physics 228 (2009) 2739–2757.
[3] https://github.com/nekStab/LightKrylov