Large eddy simulations of inhomogeneous high-magnetic Reynolds number magnetohydrodynamic flows

Abstract

Large eddy simulations of high-magnetic Reynolds number (Rem) inhomogeneous magnetohydrodynamic (MHD) flows are performed. Dynamic Smagorinsky sub-grid scale model is used for closure. A hybrid formulation of spectral and finite difference methods is developed to carry out the simulations. The current code is validated by comparing it to the previously published benchmark channel flow results. The simulations are carried out at a bulk Reynolds number of 2200 and a unity magnetic Prandtl number for increasing values of interaction parameters. This paper aims to explore the effect of velocity shear on initially band or striae-type structure of magnetic field, using MHD simulations at Rem of 2200 for low (0.0088) and high (0.5) interaction parameters (N). The flow is analyzed by plotting mean quantity variations with time and in the inhomogeneous direction, spectra of (a) kinetic and magnetic energy; (b) transfer of energy from large to small scales; and (c) transfer of energy between kinetic and magnetic field. It is observed that for higher interaction parameter, the transition from laminar to turbulent is inhibited, while for the lower value, a turbulent state is observed. The final state for N= 0.0088 is characterized by a homogeneous distribution of large and small scales formed due to the breakdown of initial striae or laminar structures as seen from the distribution of x-direction magnetic field, iso-surface plots of current density, and the second invariant of velocity gradient tensor.