This work is devoted to the studies of optimal perturbation and its transient growth characteristics in the Poiseuille flow with Reynolds number R = 1000 and with crossflow. The crossflow Reynolds number R _v , based on the uniform velocity in the negative normal direction, is varied from 0 to 200. The numerical result shows that the crossflow enhances the transient growth for three-dimensional disturbance case when . Seen from the contours of optimal energy growth in the wave number plane, the optimal perturbation that corresponds to the peak value of optimal growth becomes oblique perturbation, when crossflow is introduced. The corresponding streamwise wave number α _P increases continuously with increasing R _v , while spanwise wave number β _P drops firstly with increasing R _v and later increases. The comparison of exponential growth and transient growth is performed. It is observed that exponential growth becomes profound and even predominant over transient growth after a short period when the crossflow is sufficiently strong. Moreover, the mechanism of transient growth is discussed and it is found that the uniform crossflow can not cause transient growth in the absence of shear in basic flow. With increasing R _v , the Orr mechanism becomes more and more important relative to lift-up mechanism for the transient growth of optimal perturbation.

这项工作致力于研究雷诺数R  = 1000 和横流的泊肃叶流中的最佳扰动及其瞬态增长特性。横流雷诺数R _v基于负法线方向的均匀速度，从 0 到 200 变化。数值结果表明，当 时，横流增强了三维扰动情况下的瞬态增长。从波数平面内最佳能量增长的等高线看，当引入横流时，与最佳增长峰值相对应的最佳扰动变为斜向扰动。相应的流向波数α _P随着R 的增加而不断增加 _v ，而展向波数β _P先随着R _{v 的}增加而下降，然后再增加。进行指数增长和瞬时增长的比较。据观察，当横流足够强时，指数增长在短时间内变得深刻，甚至超过瞬时增长。此外，讨论了瞬态生长的机理，发现在基本流中没有剪切的情况下，均匀横流不会引起瞬态生长。随着R _{v 的}增加，Orr 机制相对于提升机制对于最优扰动的瞬态增长变得越来越重要。