Spatial periodicity of spatially evolving turbulent flow caused by inflow boundary condition

Space-time evolution of a flow in a semi-infinite circular pipe {x⩾0,y2+z2⩽R2} is investigated via direct numerical simulations. The unsteady turbulent inflow velocity u∣x=0 is extracted from a streamwise-periodic auxiliary simulation. It is shown that at t≫0 spatially evolving flow does not depend on initial state u∣t=0. It takes the form of spatially periodic flow of the auxiliary simulation with superimposed spatially growing perturbation. The amplitude of the perturbation increases exponentially with distance from the inlet. The growth rate is estimated for the considered Reynolds number. The obtained results suggest that the memory of the inflow boundary condition in spatial simulations is evident for a significant distance from the inlet. In the considered case an almost periodic flow is established (with less than 1% relative deviation from the periodicity) over a distance as large as 70 pipe radii.