The locking-on of vortex shedding due to the cross-stream vibration of circular cylinders in uniform and shear flows

Abstract

The frequencies of vortex shedding from circular cylinders forced to oscillate transversely in low-turbulence uniform and shear flows were investigated. The stream velocity in the shear flow varied linearly with spanwise distance. In both flows the vortex shedding frequency locked on to the cylinder frequency and to submultiples of the cylinder frequency. In uniform flow the range of cylinder frequencies for locking-on was dependent on the amplitude of oscillation and Reynolds number. At the boundaries of locking-on at the cylinder frequency locked-on shedding was intermittent with unforced shedding and locking-on was accompanied by a change in wake width. At a particular cylinder frequency near mid-range it is conjectured that the wake width jumped from being greater to being less than that for the stationary cylinder. In shear flow the spanwise extent of locking-on at the cylinder frequency was explained by considering the uniform flow results and the inclination of shed vortices in shear flow. At the spanwise boundaries of this locking-on, locked-on cells were shed intermittently with unforced cells which were more stable in frequency than the corresponding cells for the stationary cylinder.