Kinematic transitions of freely rising cylinders over a wide range of Galileo numbers

This study investigates the kinematic transitions of freely rising cylinders in quiescent fluid, focusing on the evolution of their two-dimensional motion over a wide range of Galileo numbers (275<Ga<20 000) and density ratios (ρ* =0–1). As Ga increases or ρ* decreases, the cylinder motion transitions from rectilinear ascent to vigorous oscillation, accompanied by an increase in normalized lateral amplitude (A*) and a decrease in the Froude number (Fr). However, the interdependence between Ga and ρ* complicates the isolation of their individual effects. To overcome this limitation, we revisit the dimensional analysis and introduce a new pair of dimensionless parameters: Ga and the dimensionless kinematic viscosity (ν*), which allow independent control and clear interpretation of the transition behavior. Experiments conducted at fixed ν* show that increasing Ga induces the transition, while increasing ν* shifts the transition to lower Ga values. Based on these findings, we propose an effective Galileo number, Gaeff, that integrates the effects of Ga and ν*. This new parameter accurately predicts the onset of kinematic transitions across a wide range of fluid viscosities and captures the associated variations in A*, Fr, and the drag coefficient.