Characterization of the lid-driven cavity magnetohydrodynamic flow at finite magnetic Reynolds numbers using far-field magnetic boundary conditions

The lid-driven cavity (LDC) flow is a canonic hydrodynamic problem. Here, a 3D LDC flow of electrically conducting, incompressible fluid is studied numerically in the presence of a strong magnetic field, which is applied parallel to the lid plane and perpendicular to the direction of the lid motion. The cavity has electrically conducting walls of finite thickness and an infinitely thin moving lid. The problem is characterized by three dimensionless parameters: the Reynolds number (Re), the Hartmann number (Ha), and the magnetic Reynolds number (Re_m). The primary research focus is on the effect of Re_m, which was changed in the study from Re_m ≪ 1 to the maximal Re_m = 2000 at which dynamo action may be expected, while Ha = 100 and Re = 2000. The computational approach is based on the utilization of far-field magnetic boundary conditions by solving the full magnetohydrodynamic (MHD) flow problem at finite Re_m for a multi-material domain composed of the inner conducting liquid, conducting walls, and sufficiently large insulating outer domain called "vacuum" (the induced magnetic field vanishes at the vacuum boundaries) using a fractional-step method. The computed results show many interesting features with regard to the effect of Re_m on the MHD boundary layer and the bulk flow, generation of a magnetic field and its penetration into vacuum, energy balance, tendency of the magnetic field to become frozen in the fluid and associated magnetic flux expulsion, transition to unsteady flows, and self-excitation of the magnetic field and the associated dynamo-type action at high Re_m.