Observability of periodic lines in three-dimensional lid-driven cylindrical cavity flows

Abstract

This study employs three-dimensional particle-tracking velocimetry (3D-PTV) for experimental investigation of the existence and properties of periodic lines in 3D lid-driven time-periodic flows inside a cylindrical cavity. These periodic lines, consisting of material points that periodically return to their initial position, play a central role in the transport properties of laminar flows, yet their existence has so far been demonstrated only in numerical simulations. The formation and characteristics of periodic lines are inextricably linked with spatiotemporal symmetries of the flow. 3D-PTV measurements determined that relevant symmetries, identified with previous symmetry analyses, are satisfied within experimental error bounds. These measurements subsequently isolated periodic lines in the designated symmetry planes, thus offering first experimental evidence of their physical existence and their fundamental reliance on symmetries. Experimental periodic lines are topologically equivalent to those in simulated flows with identical symmetries and exhibit the same response to changes in forcing conditions. The laboratory experiments by these observations bridge the gap from theoretical and numerical predictions on periodic lines to real 3D flows.