Effects of a streamwise magnetic field on the exact coherent states in a channel flow

Abstract

This study provides a comprehensive investigation into the influence of a uniform, constant streamwise magnetic field on Exact Coherent States (ECS) in channel flows, an area unexplored within magnetohydrodynamic (MHD) research compared to spanwise or wall-normal magnetic field orientations. Utilizing direct numerical simulation and the standard bisection method, we examine ECS behavior across a range of computational domains with Reynolds numbers Re spanning from 3000 to 9000 and Hartmann numbers Ha ranging from 0 to 100. The results reveal a previously unobserved second saddle-node bifurcation of ECS with respect to Ha, occurring around Ha = 30 – 0.002Re for Re > 4000. This phenomenon is unique to the streamwise magnetic field configuration, and is absent under either spanwise or wall-normal magnetic fields. Additionally, the streamwise magnetic field prolongs the cycle time of relative periodic orbits (RPOs), contrasting with the cycle time reduction typically induced by other magnetic orientations, and induces a more gradual decay of streamwise perturbation energy, sustaining streamwise streaks in the channel flow. Furthermore, it is observed that, at Re = 6000 and Ha = 10, RPOs bifurcate into traveling waves (TWs) as the spanwise domain length Ly reaches approximately 2.683, with TWs remaining spanwise localized as Ly increases further.