Dynamics of a rising and falling cylinder

In the present investigation, we study the dynamics of a cylinder which is allowed to rise or fall freely through a fluid. We find that falling cylinders, oriented horizontally, all descend in a rectilinear path. As one reduces the relative density (or mass ratio, m*m*), such that m*<1m*<1 and the cylinders begin to rise, rectilinear trajectories are found to persist. However, when one falls below a special value of the relative density, the body suddenly commences large-amplitude transverse vibration, with horizontal fluctuations of nearly 2 diameters peak-to-peak. It turns out that the critical mass ratio for this phenomenon to appear, mcrit*=0.54, agrees remarkably well with the critical value for elastically mounted cylinders, defining a similar sudden transition between states. The vigorously vibrating cylinder exhibits a 2P mode of vortex formation, as found previously for elastically mounted bodies in purely transverse motion. This is consistent with the fact that the critical values of relative densities are similar, although the closeness of the values is unexpected when one considers that the freely rising body exhibits streamwise motions. It appears that the existence of a critical relative density for the rising cylinder is a new phenomenon.