EXACT COHERENT STATES IN CHANNEL FLOW UNDER NORMAL MAGNETIC FIELD

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. The exact coherent states-periodic orbits solution with different Reynolds number and Hartmann number combinations are found in plane Poiseuille flow by using direct numerical simulation combined with bisection method. Then compared the structure and morphology of these solutions under the parameter combination considered. According to the results, they are not significantly different whether a normal magnetic field is applied. All of them consist of streaks and vortices on both sides which located in the center of the channel. The period increases and the amplitude decreases with the Reynolds number. The perturbation energy in all directions oscillates periodically, the coherent structure migrates to the wall on both sides and the amplitude of disturbance velocity increases with the strength of magnetic field increasing. The perturbation energy of the exact coherent state is proportional to Re^−2.36 when there is no magnetic field and the rescaled rms amplitudes at different Reynolds number are similar. The above scaling law does not change but the rms velocity distribution is not similar anymore and the perturbation energy of the exact coherent state increases with the magnetic field strength. It indicates that the magnetic has a certain suppression of the disturbance so that the flow field remains relatively stable.