The Prominent Role of the Upstream Conditions on the Large-scale Motions of a Turbulent Channel Flow

In this study we investigate how upstream perturbations in a turbulent channel flow impact the downstream flow evolution, especially the large-scale motions. Direct numerical simulations were carried out at a friction Reynolds number, $Re_{\tau}=394$. Spanwise varying inlet blowing perturbations were imposed at 1$\pi h$ from the inlet. The flow field is decomposed into its constituent scales using proper orthogonal decomposition. The large-scale motions and the small-scale motions of the flow field are separated at a cut-off mode number, $M_c$. The cut-off mode number is defined as the number of the mode at which the fraction of energy recovered is $55\%$. It is found that Reynolds stresses are increased due to blowing perturbations and large-scale motions are responsible for more than $70\%$ of the increase of the streamwise component of Reynolds normal stress. Surprisingly, $90\%$ of Reynolds shear stress is due to the energy augmentation of large-scale motions. It is shown that inlet perturbations impact the downstream flow by means of the LSM.