Effect of nonlinear interaction on feedback control of wall turbulence

Abstract

Direct numerical simulation of turbulent channel flow at Reτ = 110 ~ 650 was made in order to evaluate feedback control algorithms for reducing skin friction. The energy efficiency of the v-control and suboptimal control is deteriorated with increasing the Reynolds number, but it becomes almost constant above Reτ = 300. It is found through the Karhunen-Loeve decomposition of the turbulent fluctuations that the structures having large contribution to the turbulent kinetic energy are of large scale, whilst the structures having large contribution to the wall shear stress fluctuation are scaled with viscous units and accompanied with the quasi-streamwise vortices near the wall. The KL modes are divided into groups depending on the wall elevation of the structures, and the nonlinear interaction between those structures are examined. It is indicated that the interaction effect is larger at higher Reynolds numbers, but the near-wall vortices are not much affected by the interaction with the large-scale outer structures.