Simulation of Confined Magnetohydrodynamic Turbulence This proposal addresses the modeling and numerical simulation of magnetohydrodynamic (MHD) turbulence in bounded domains. For this purpose we propose to combine a highly efficient pseudo-spectral method with a volume penalization technique to take into acount the geometry of the domain together with appropriate boundary conditions.
We have already successfully used this method to compute turbulent fluid flows and we will generalize it to study turbulent MHD flows. Preliminary studies in two and three dimensions have proven the feasability of the approach to study MHD turbulence. The potential of the proposed method is twofold. First the geometry of the confining domain can be easily modified to almost arbitrary complex shapes without changing the numerical code. Second, the use of the Fourier spectral discretization allows the simulation of parameter ranges (such as the Reynolds number) which are beyond reach with the currently available schemes.
A first part of the project will be devoted to a detailed validation of the method. In this validation stage a particular attention will be given to the boundary conditions for the magnetic field. In contrast to the velocity, the magnetic field does not trivially vanish at the boundaries. Different types of boundary conditions will be investigated, implemented and their compatibility with the penalization method will be assessed. Subsequently the numerical codes in which we integrate the penalization method will be optimized and implemented on the CNRS massively parallel computers.
After this validation phase simulations will be performed to investigate three distinct physical problems. The first application is the study of the dynamo problem which concerns the self-amplification of a magnetic field. The present approach will allow to gain understanding on the recent observations of magnetic-field amplification in experimental dynamos, by simulating high Reynolds number MHD turbulence in a wall bounded geometry similar to the one used in experiments (such as the Sodium von Karman flow of the dynamo experiment at CEA-Cadarache).
The second application is the investigation of Alfvén wave propagation and reflection. Indeed, the presence of a magnetic field in a conducting fluid allows the presence of waves, which play a keyrole in the dynamics of MHD turbulence. A comparison with the reflection of Alfvén waves in the current Gallium experiments in Grenoble will allow to progress our understanding of the linear and nonlinear effects which govern MHD turbulence.
The third application is the self-organization of MHD turbulence in toroidal geometry. We recently showed that a two-dimensional plasma flow spontaneously spins up in a non-axisymmetric geometry, which is not the case in an axisymmetric geometry. The shape of the container thus seems to play a critical role with respect to the large scale velocity fields. The extension of this study to three dimensions will allow to check the possibility that three dimensional toroidally confined MHD turbulence self-organizes into a spontaneously rotating state. Implications for the self-organization and intrinsic rotation of fusion plasmas will be investigated.
