The rich life of light rising spheres

Abstract

The straight path of spheres falling or rising in a weakly viscous fluid is known to become unstable beyond a critical value of the so-called Archimedes number Ar, a Reynolds number built on the gravitational velocity scale. Various styles of non-vertical paths have been reported so far: steady or oscillating oblique, planar zigzags, three-dimensional chaotic, etc. However despite careful computations and experiments, there is currently no consensus as regards the possible critical density ratio m* below which significant departures from straight (vertical or oblique) path are observed. To revisit this question, we carry out a detailed DNS study focused on rising spheres (m*\textless 1) in the range 150 ≤ Ar ≤ 350. Non-straight paths with significant horizontal excursions are observed throughout the whole range of m*. In addition to the various aforementioned types of paths we also identify other styles such as intermittent zigzagging/oblique paths and find that very light spheres describe highly nonlinear zigzags and have drag coefficients up to 15{\%} beyond standard values.