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

Abstract

This study investigates the kinematic transitions of freely rising cylinders in quiescent fluid, focusing on the evolution of their twodimensional motion over a wide range of Galileo numbers (275 < Ga < 20 000) and density ratios (q ¼ 0–1). As Ga increases or q 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 q 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 (), which allow independent control and clear interpretation of the transition behavior. Experiments conducted at fixed show that increasing Ga induces the transition, while increasing 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 . 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.