Exact Coherent States in Large Computational Domains Under Normal Magnetic Field

The understanding of turbulence dynamics and subcritical transitions in fluid flow is of significant importance in various scientific and engineering fields. This paper explores the influence of a normal magnetic field on the exact coherent state and its structures within a large computational domain. By employing direct numerical simulation and the bisection method, exact coherent structures are calculated at different computational domain sizes for a fixed Reynolds number Re = 3000. It is observed that as the spanwise dimension of the domain increases, the periodic orbital bifurcation transforms into a saddle-node bifurcation, and the periodic orbital solution is replaced by traveling wave solution with localized flow structures. The introduction of a normal magnetic field does not alter the localization state in the flow field significantly. However, the presence of vortices becomes more pronounced on both sides compared to the scenario without a magnetic field.