Lagrangian transport in two‐dimensional time‐periodic cavity flow

Abstract

The Lagrangian transport in a laminar incompressible flow in a two-dimensional square cavity driven by a harmonic tangential oscillation of a single cavity wall is investigated numerically for a range of Reynolds (Re) and Strouhal (Str) numbers. The topology of fluid trajectories is described by means of stroboscopic projections, which reveal the co-existence of chaotic trajectories and regular Kolmogorov-Arnold-Moser (KAM) tori. The higher the frequency of the lid oscillation the more regular the fluid motion becomes and the size of the KAM tori increases. For low frequencies the KAM tori are strongly stretched along instantaneous streamlines of the flow, while for high frequencies they resemble streamlines of a mean flow.