Effect of normal magnetic field on the exact coherent state of channel flow at large Reynolds number

Abstract

Abstract Laminar-turbulent subcritical transition has been always a hot issue in fluid mechanics. Exact coherent states are important for predicting the path of transition and understanding the cycle of turbulent self-sustaining process. One of the most common methods of investigating subcritical transition is dynamical system method and many different forms of invariant solutions have been obtained in many shear flows. In order to study the effect of magnetic field on the exact coherent state of channel flow at large Reynolds number, the direct numerical simulation combined with bisection method is used to calculate the exact coherent state-periodic orbit solution with different magnetic field strength at Re ⩾ 9000, and the structure and morphology in the flow field are compared. The results show that the magnetic field strength does not change the structure and shape of the solution and the scaling law between the transition threshold and Reynolds number does not change significantly, which shows obviously self-similarity. As the magnetic field strength increases, the period of the exact coherent state decreases and the perturbation energy in each direction exhibits periodical oscillation changes. In addition the shape of the amplitude curve also changes due to the magnetic field effect. The above results show that the magnetic field has a certain inhibition effect on the disturbance at large Reynolds number, and the flow field remains relatively stable.