Modulation and classification of wake transitions through vortex evolution phases in undulated cylinders at low Reynolds number

This study examines how wavy orientation and undulation-induced geometric variations regulate vortex formation, wake transitions and aerodynamic performance in sinusoidally wavy cylinders. Using three-dimensional (3-D) simulations at a Reynolds number Re = 100, we analyse the transition from two-dimensional (2-D) to 3-D wakes across varying spanwise wavelengths and undulation configurations. A novel framework is introduced for classifying vortex structures, analyisng centreline trajectories and decomposing vortex structures, revealing how geometric variations induce distinct 3-D vortical structures. At short wavelengths, vortices originate from bluff regions and diminish in a continuous manner, stabilising the wake. At longer wavelengths, phase-dependent vortex onset leads to localised interactions, disrupting wake coherence and delaying stabilisation. A key discovery is the role of transverse recirculating flow in wake stabilisation, which induces reverse impingement, redirects fluid and weakens spanwise vortex coherence. Additionally, wavy orientation strongly influences vortex evolution and dislocation, altering vortex trajectories and wake stability. To further clarify these wake transitions, a classification framework is introduced, defining distinct phases such as vortex stretching, break-up and re-symmetrisation. The relationship between force characteristics and wake stabilisation is also established, with wavy orientation and undulation geometry regulating the transition from quasi-2-D spanwise vortical flow to 3-D spiral flow. A critical wavelength is identified where drag and lift fluctuations are minimised, with elliptical-section undulations achieving superior aerodynamic performance through enhanced vortex synchronisation. These findings provide new insights into vortex control strategies, with applications in bio-inspired propulsion, passive flow control and energy-efficient aerodynamic designs across engineering and industrial fields.