Critical mass and a new periodic four-ring vortex wake mode for freely rising and falling spheres

In this letter, we study the dynamics and vortex wakes of spheres rising or falling freely through a fluid. Since this problem was first considered by Newton in 1726, the conditions under which a sphere will vibrate are still not understood clearly. In our experiments, all falling spheres (where the relative density, $m∗>1$⁠) descend rectilinearly. Although previous studies conclude that all rising spheres $(m∗<1)$ vibrate, we find instead that there exists a critical value of the relative density (for example, $mcrit∗=0.36$⁠, for Reynolds numbers 400–500) above which there is a significant regime where rising spheres do not vibrate. Lighter spheres undergo large-amplitude periodic oscillations, confined to a single vertical plane. We discover a new mode of vortex formation comprising four vortex rings formed in each cycle, distinct from previous vortex modes for fixed and tethered bodies.