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The tip leakage vortex (TLV), which develops in the clearance between the blade tip and the casing of axial turbomachines, appears in many industrial applications, such as air transportation, space rockets and hydraulic machines. In the latter, cavitation may develop in the core of the TLV, often leading to severe erosion of the runner blades and the casing. Despite the progress achieved in understanding and controlling the dynamics of this particular flow, many associated phenomena are still not sufficiently explored. It remains, for instance, unclear how the clearance size is related to the occurrence of cavitation in the TLV. The present work contributes to this research by assessing the effect of the clearance size on the TLV intensity and dynamics in a simplified case study. The vortex is generated by a two dimensional generic blade in a water tunnel, while the clearance between the blade tip and the wall is varied. The properties of the TLV are established with the help of stereo-PIV and flow visualizations for a wide range of incidence angles, inlet velocities and tip clearances. The measurements clearly reveal the existence of a specific tip clearance for which the vortex intensity is at its maximum and most prone to generate cavitation. By introducing a new dimensionless coefficient $\tau/\Gamma^*_{\infty}$, where $\tau$ is the normalized clearance and $\Gamma^*_{\infty}$ is the normalized circulation in the unconfined case, it is established that the TLV circulation reaches a peak intensity for $\tau/\Gamma^*_{\infty}\approx0.2$, the amplitude of which is in average 45 ($\pm$10) \% higher than in the unconfined case, regardless of the operating conditions. The change in the vortex structure due to cavitation occurrence is also investigated in a different case study by means of PIV using fluorescent seeding particles. A vortex is generated by an elliptical hydrofoil and the velocity field outside the vapor phase is compared with the one in cavitation-free conditions. It is found that the cavitation does not change the vortex circulation, since the tangential velocity distribution of the cavitating vortex is identical to the non-cavitating vortex far from the vapor core. The tangential velocity close to the vapor core is however lower than in cavitation-free conditions. Moreover, the fluid is in solid body rotation in the vicinity of the liquid-gas interface. The alteration of the clearance geometry with shallow grooves to manipulate the gap flow and control the TLV intensity is evaluated in the simplified case study. The cavitation in the TLV and in the clearance region is significantly reduced with grooves located near the foil leading edge, oriented at 45$^{\circ}$ or 90$^{\circ}$ relative to the incoming flow. This result paves the way for further investigations, which may ultimately lead to TLV cavitation mitigation in axial turbines.