Lagrangian Coherent Structures and the Organization of Transport and Mixing in a Transitional Cylinder Wake (Re = 500)

Understanding how unsteady flow structures control transport and mixing in cylinder wakes is essential for predicting dispersion, heat transfer, and fluctuating forces in many engineering and environmental systems. In this study, we examine the two-dimensional wake of a circular cylinder at a moderate Reynolds number of 500 to determine how coherent flow structures shape entrainment, vortex formation, and downstream mixing. The unsteady flow is computed using a high-resolution finite-element solver, and material transport is analyzed through the extraction of time-dependent stretching patterns that identify repelling and attracting surfaces in the flow. These surfaces provide a direct picture of how fluid parcels are directed, trapped, or released as the wake evolves. The results show that the interaction of repelling and attracting material surfaces governs the timing and geometry of vortex roll-up, the formation of distinct vortical packets, and the onset of chaotic advection farther downstream. Localized mixing hot spots emerge as narrow regions of intense stretching between alternating vortices—features that are not visible from instantaneous flow fields alone. Quantitatively, the computed vortex-shedding frequency corresponds to a Strouhal number of approximately 0.21, consistent with established values for cylinder wakes at this flow regime and confirming the accuracy of the simulation. The study demonstrates that examining the wake through its underlying material structures provides a clearer and more physically transparent interpretation of transport and mixing than traditional instantaneous diagnostics. The novelty of this work lies in treating these material surfaces as the primary organizational framework of the wake and in showing how they determine preferential entrainment routes and dominant mixing pathways. This perspective offers a foundation for developing future strategies aimed at enhancing scalar transport or reducing unsteady loading in flows around bluff bodies.