Wake dynamics of a square cylinder while moving upward in quiescent water

Abstract

We experimentally investigate the wake dynamics of a square cylinder rising through quiescent water over a range of Froude numbers ($\mathrm{Fr}$). Time-resolved Particle Image Velocimetry provides velocity and vorticity fields that enable pressure reconstruction and vortex characterization. Diagnostics based on swirl strength ($λ_{ci}$), the Okubo-Weiss parameter ($W$), and a shear-vortex interaction measure ($Λ$) reveal that the wake is governed by a persistent pair of counter-rotating vortices rather than by periodic shedding. Circulation exhibits a two-regime dependence on $\mathrm{Fr}$, with a sharp increase below $\mathrm{Fr}\approx 1$ and saturation above this threshold, mirroring entrainment force scaling reported previously. While vortex area remains nearly constant, swirl strength and negative-$W$ regions expand with $\mathrm{Fr}$, indicating that entrainment enhancement arises from intensified rotation rather than an enlarged vortex footprint. These findings provide new physical insight into vortex-free-surface interactions and enrich the understanding of entrainment mechanisms in unsteady wakes, with implications for multiphase flows and the hydrodynamic design of naval and offshore structures.