Free-surface vortex in a cylinder driven by a rotating side wall

Free-surface vortices are prevalent in both natural and engineering flows, yet their transient nucleation and penetration mechanisms remain insufficiently quantified. Transient experiments, in conjunction with three-dimensional Volume of Fluid–Scale Adaptive Simulation with Curvature Correction numerical simulations, are employed to investigate the formation and evolution of free-surface vortices in a cylindrical container driven by rotating sidewalls. By controlling the angular velocity and pre-rotation duration, the nonlinear coupling between the initial angular momentum distribution and the subsequent growth of the surface depression, vortex–core contraction, and penetration timing is elucidated. Based on a modified Torricelli's law, a drainage formula for rotating systems incorporating the centrifugal press head is established. The findings indicate that vortex initiation and development are governed by a strong interplay between rotation rate and duration, with the evolution exhibiting three distinct stages: an initial slow-growth phase, a rapid-development phase, and a saturation–quasi-steady phase. Fitting with Oseen and Burgers vortex models reveals an inverse correlation between circulation and axial strain rate. Following vortex establishment, the bottom region develops a more stable core structure under centrifugal dominance, whereas the core radius near the free surface increases markedly. Moreover, turbulent kinetic energy displays a bimodal pattern prior to nucleation and penetration. Radial iso-volume annulus analysis identifies a sequentially lagged vorticity transport chain from the periphery toward the center, providing new evidence for the spatial redistribution of energy and momentum within the vortex.