The wake of falling disks at low Reynolds numbers

Abstract

We visualized the wake structure of circular disks falling vertically in quiescent water. The evolution of the wake was shown to be similar to the flow patterns behind a fixed disk. The Reynolds number, Re = Ud/ν, is in the range of 40–200. With the ascension of Reynolds numbers, a regular bifurcation occurred at the first critical Reynolds number \(Re_{c_1 }\), leading to a transition from an axisymmetric wake structure to a plane symmetric one; A Hopf bifurcation took place at the second critical Reynolds number \(Re_{c_2 }\), as the wake structure became unsteady. Plane symmetry of the wake structure was first lost as periodic vortex shedding appeared, but recovered at higher Reynolds number. The difference between the two critical Reynolds numbers was found to be shape-dependent, as we compared our results for thin discs with those for other falling bodies, such as spheres and cones. This observation could be understood in terms of the instability mechanism of the vortical structure.