Vortex formation in the wake of an oscillating cylinder

When a body oscillates laterally (cross-flow) in a free stream, it can synchronize the vortex formation frequency with the body motion frequency. This fundamental “lock-in” regions is but one in a whole series of synchronization regions, which have been found in the present paper, in an amplitude-wavelength plane (defining the body trajectory) up to amplitudes of five diameters. In the fundamental region, it is shown that the acceleration of the cylinder each half cycle induces the roll-up of the two shear layers close to the body, and thereby the formation of four regions of vorticity each cycle. Below a critical wavelength, each half cycle sees the coalescence of a pair of like-sign vortices and the development of a Karman-type wake. However, beyond this wavelength the like-sign vortices convect away from each other, and each of them pairs with an opposite-sign vortex. The resulting wake comprises a system of vortex pairs which can convect away from the wake centerline. The process of pairing causes the transition between these modes to be sudden, and this explains the sharp change in the character of the cylinder forces observed by Bishop and Hassan, and also the jump in the phase of the lift force relative to body displacement. At precisely the critical wavelength, only two regions of vorticity are formed, and the resulting shed vorticity is more concentrated than at other wavelengths. We interpret this particular case as a condition of “resonant synchronization”, and it corresponds with the peak in the body forces observed in Bishop and Hassan's work.