法向磁场作用下槽道流内的精确相干态

EXACT COHERENT STATES IN CHANNEL FLOW UNDER NORMAL MAGNETIC FIELD

层流-湍流转捩过程一直以来都是流体力学的研究热点,精确相干态对于预测转捩路径和理解湍流自维持动力循环过程具有重要的意义.为了研究法向磁场对槽道流转捩过程的影响,文章利用直接数值模拟方法结合二分法,在槽道泊肃叶流中寻找不同雷诺数和哈特曼数组合下的精确相干态-周期轨道解,并对施加磁场前后精确相干态的结构与形态进行了对比分析.结果发现,在本文考虑的参数组合下,精确相干结构在施加磁场前后并无明显变化,均由位于通道中心的流向条带及其两侧的流向漩涡构成.随雷诺数的增大,精确相干态的轨道周期变长,而扰动能振幅则减小.当磁场强度增大时,流场内各方向上的扰动能呈周期性振荡变化,且流场内的相干结构向两侧的壁面迁移,扰动速度振幅增大.无磁场作用时,精确相干态的扰动能正比于Re^(-2.36),且不同Re数下的均方根扰动速度分布具有相似性.施加法向磁场后,上述标度律不变,均方根速度分布不再具有相似性,精确相干态的扰动能随磁场强度增加而增大,表明磁场对扰动具有一定的抑制作用,从而使流场保持相对的稳定.

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.