The patterns of vortex formation from a cylinder oscillating in a horizontal plane, located at various depths of submergence beneath a free surface, are characterized using high-image-density particle image velocimetry (PIV). Instantaneous representations of the velocity field, streamline topology and vorticity patterns are referenced to the instantaneous velocity of the cylinder. In turn, these features are related to the magnitude and phase of the instantaneous transverse force, which can exhibit highly nonlinear, spike-like fluctuations. When a finite gap is maintained between the free surface and the cylinder, the patterns of vorticity concentrations are altered in such a fashion that both the peak magnitude and the degree of amplitude modulation of the negative transverse force spikes are attenuated, but shifted little in phase, relative to the case of the fully submerged cylinder. On the other hand, when the cylinder is sufficiently close to the free surface such that the gap region is eliminated, the patterns of vorticity concentrations are fundamentally different and the negative transverse force spikes are remarkably more pronounced and consistent than for deeper submergence.