Drag reduction characterizations of turbulent channel flow with surfactant additive by proper orthogonal decomposition and wavelet transform

To explore the drag-reducing characteristics of turbulent channel flows with surfactant additive at relatively high Reynolds number from the perspectives of energy spectrum and multi-scale resolution, the two-dimensional fluctuation velocity fields of turbulent channel flows with/without surfactant additive at Reynolds number of Reτ = 590 obtained by large eddy simulation are decomposed by two-dimensional proper orthogonal decomposition (POD) and wavelet transform (WT). POD results show that the low-order eigenmode occupying most energy can be used to capture large-scale vortex structures, and fewer eigenmodes can be employed to capture coherent structures (CSs) in surfactant solution case compared with that in the Newtonian fluid. The spatial structures depicted by POD eigenmode state that buffer layer has a tendency to move towards the center of the channel in surfactant solution. Through wavelet analysis of fluctuation velocity fields in the streamwise-wall-normal planes, it is found that CSs mainly distribute in the near-wall region and the amount of CSs is smaller in surfactant solution. The results of local Reynolds shear measure (LRM) show that local contribution of CSs to the intermittency in turbulent channel flow of surfactant solution decreases, indicating the inhibition of intermittency by surfactant additive. In order to investigate the drag-reducing characteristics at different locations along the wall-normal direction, the fluctuation velocity fields in the streamwise-spanwise planes at different wall-normal locations are decomposed by two-dimensional WT. The results show that surfactant additive mainly affects the flow in the near-wall region (especially in the buffer layer) and thus induces drag reduction effect.