The mechanisms of laminar-turbulent transition in the MHD pipe flow subject to a transverse magnetic field

This study focuses on the mechanisms behind laminar-turbulent transition in the magnetohydrodynamic (MHD) pipe flow in the presence of a transverse magnetic field. In contrast to the hydrodynamic pipe flow, the MHD flow may become linearly unstable owing to the modification of the base flow by the magnetic field. The instability typically occurs when weak velocity jets in the base velocity profile are present and is restricted to certain regimes of the flow when the Reynolds and Hartmann numbers are sufficiently high and the wall of the pipe is electrically conducting. Therefore, subcritical transition induced by perturbations of finite amplitude that arise due to significant transient growth of initially small disturbances may also play a signifcant role. In this context, a three-dimensional perturbation that exhibits the largest transient amplification is then referred to as an optimal perturbation.

Here we exploit global modal and non-modal stability analyses to study the two scenarios of transition numerically. This allows us to identify the most dangerous disturbances predicted by the two theories. The non-linear evolution and transitional flow dynamics of the MHD pipe flow subject to the optimal perturbation is then studied using direct numerical simulation.