Optimal perturbations in viscous channel flow with crossflow

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 Rv < 17.9. 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.