Numerical simulation of a two-dimensional turbulence experiment in magnetohydrodynamics

Publisher Website
Google Scholar
Abstract
Numerical simulations of a two-dimensional turbulence experiment within a confined domain are presented. The setup consists of a layer of mercury enclosed in a square box and driven by the injection of electric currents in a uniform magnetic field. The numerical finite difference model simulates the Navier–Stokes equation in two dimensions with steady forcing and linear bottom friction. Subgrid scales are modeled by an artificial constant viscosity or a higher order (biharmonic) lateral friction. The model provides an accurate representation of the (inverse) transfers of energy from the forcing scale toward the size of the domain. These transfers lead to the spontaneous appearance of a mean rotating flow, when dissipation is sufficiently weak. Thin vorticity sheets are shown to have an important role for the dynamics of the large scales. Therefore a critical spatial resolution, increasing with the bottom friction time scale, is required to get an accurate calculation. The requirement of a high resolution could not be avoided by means of the subgrid scale dissipation. Furthermore, for some low values of the dissipation, a second flow regime, without laboratory counterpart, is obtained.