Transient dynamics of a rotating triangular free-surface polygon in a cylindrical tank

This study investigates the transient and post-transient dynamics of a rotating triangular free-surface polygon in a viscous glycerol–water mixture liquid driven by a linearly spinning-up disk inside a cylindrical tank. The dynamics of rotating fluid is numerically computed by large eddy simulation (LES) and validated thoroughly by precise measurements of the full free-surface height field. The time evolution of the free surface reveals that the whole dynamic process can be divided into two stages: an initial global surface deformation stage to achieve the nearly axisymmetric baseflow, followed by a subsequent non-axisymmetric instability growth and saturation stage to a periodic flow. Proper orthogonal decomposition (POD) of the velocity fields is applied to extract the dominant spatial structures and their corresponding time coefficients. The entire transient dynamics can be modeled with the mean-field model with only two oscillatory fast variables and a slow variable, where sparse Galerkin regression is proved to capture accurately the nonlinear saturation process. This work bridges experimental and numerical studies of a benchmark rotating triangular configuration and demonstrates the potential of data-driven reduced-order modeling for elucidating rotating polygonal instabilities.