Decay of isotropic flow and anisotropic flow with rotation or magnetic field or both in a weakly nonlinear regime

Abstract

We investigate numerically the decay of isotropic, rotating, magnetohydrodynamic (MHD), and rotating MHD flows in a periodic box. The Reynolds number $Re$ defined with the box size and the initial velocity is $100$ at which the flows are in a weakly nonlinear regime, i.e. not laminar but far away from the fully turbulent state. The decay of isotropic flow has two stages, the first stage for the development of small scales and the second stage for the viscous dissipation. In the rapidly rotating flow, fast rotation induces the inertial wave and causes the large-scale structure to inhibit the development of the first stage and retard the flow decay. In the MHD flow, the imposed field also causes the large-scale structure but facilitates the flow decay in the first stage because of the energy conversion from flow to magnetic field. Magnetic Reynolds number $Rm$ is important for the dynamics of the MHD flow, namely a high $Rm$ induces the Alfv\'en wave but a low $Rm$ cannot. In the rotating MHD flow, slower rotation tends to convert more kinetic energy to magnetic energy. The orientation between the rotational and magnetic axes is important for the dynamics of the rotating MHD flow, namely the energy conversion is more efficient and the stronger wave is induced when the two axes are not parallel than when they are parallel.