Interaction between a large-scale structure and near-wall structures in channel flow

Direct numerical simulation of a turbulent channel flow in a periodic domain of relatively wide spanwise extent, but minimal streamwise length, is carried out at Reynolds numbers $\Rey_\tau\,{=}\,137$ and 349. The large-scale structures previously observed in studies of turbulent channel flow using huge computational domains are also shown to exist even in the streamwise-minimal channels of the present study. Moreover, the limitation of the streamwise length of the domain enforces the interaction between large-scale structures and near-wall structures, which consequently makes it tractable to extract a simple cycle of processes sustaining the structures in the present channel flow. It is shown that the large-scale structures are generated by the collective behaviour of near-wall structures and that the generation of the latter is in turn enhanced by the large-scale structures. Hence, near-wall and large-scale structures interact in a co-supporting cycle.