Direct numerical simulation as a tool for understanding MHD liquid metal turbulence

Abstract

The method of direct numerical simulation (DNS) is applied to investigate the most general properties of turbulent flows of liquid metals in the presence of a constant magnetic field. Various aspects of the flow transformation into an anisotropic state are thoroughly examined. The flow is assumed to be homogeneous and the problem is reduced to the classical case of a turbulent flow in a 3D box with periodic boundary conditions. In the framework of this formulation, three specific types of the flow are considered, which are the forced flow, thermal convection, and freely decaying flow. To investigate the long-time evolution of an initially isotropic flow a large-scale forcing is applied to maintain the flow energy at a statistically steady level. The evolution is found to depend strongly on the magnetic interaction parameter (Stuart number). In the case of small Stuart number, the flow remains three-dimensional, turbulent, and approximately isotropic. At large Stuart number (strong magnetic field) the turbulence is suppressed rapidly and the flow becomes two-dimensional and laminar. Very interesting is the intermittent flow evolution detected at moderate Stuart number. Long periods of almost two-dimensional, laminar behaviour are interrupted by strong turbulent three-dimensional bursts. The influence of a constant magnetic field on scalar transport properties of liquid metal turbulence is investigated using the simplified formulation of a homogeneous flow driven by an imposed mean temperature gradient. The flow structure is dominated by two turbulent antiparallel jets providing an effective mechanism of heat transfer. It is shown that the magnetic field parallel to the mean temperature gradient stabilizes the jets and, thus, enhances heat transfer considerably. In the third part, freely decaying MHD turbulence is considered. Numerical simulations are applied to verify the theoretical model proposed in [J. Fluid Mech. 336 (1997) 123]. In particular, it is confirmed that the structure of viscous dissipation and evolution of perpendicular length scale are affected only slightly by the magnetic field. A simple approximation for the mean Joule dissipation is proposed.