Wake-induced forces and torques on a zigzagging/spiralling bubble

The numerical results obtained by Mougin & Magnaudet (Phys. Rev. Lett. vol. 88, 2002a, 14502) for the flow past a freely moving spheroidal bubble with a prescribed spheroidal shape are processed to analyse the evolution of the forces and torques experienced by the bubble when it rises along a planar zigzag and a circular helix. It is found that, as soon as the wake becomes three-dimensional, a lateral force with a strength comparable with that of the buoyancy force occurs. This force, together with the corresponding torque, drives the horizontal movements of the bubble. The force and torque balances reveal how these wake-induced effects are balanced by added-mass effects to make possible the existence of zigzag and helical motions along which the angle between the velocity and the symmetry axis of the bubble remains small. The evolution of the wake during the zigzag indicates that the sign of the trailing vortices, and thus that of the wake-induced force and torque, is governed by the rotation of the bubble and reveals the sensitivity of the wake dynamics to the changes in the bubble velocity and rotation rate.