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In this paper, we numerically study the oscillatory dynamics associated with the tip vortex cavitation over an elliptical hydrofoil section using our 3D variational multiphase flow solver at a Reynolds number of $Re=8.95 \times 10^5$ via dynamic subgrid-scale modeling and homogeneous mixture theory. To begin, we examine the grid resolution requirements and introduce a length scale that considers both the tip vortex strength and the core radius, which is then employed to non-dimensionalize the spatial resolution in the tip vortex region and establish mesh requirements for large eddy simulation of tip vortex cavitation. We next perform simulations to analyze the dynamical modes of cavity oscillation at different cavitation numbers and compare them with the semi-analytical solution. The breathing mode of cavity surface oscillation is extracted from the results through the definition of an effective radius. The time-averaged effective radius demonstrates that the cavity experiences a growth region followed by decay as it progresses away from the tip. Further examination of the local breathing mode oscillations in these regions indicates the different behavior of cavity oscillations in the growth and decay regions, with the oscillations within the former being characterized by lower frequencies. For representative cavitation numbers $\sigma \in [1.2,2.6]$, we find that pressure fluctuations exhibit a shift of spectrum towards lower frequencies as the cavitation number decreases, similar to its influence on breathing mode oscillations. The results indicate the correlations between the breathing mode oscillations and the pressure fluctuations, with the low-frequency and relatively higher-frequency pressure fluctuations being correlated with the growth and decay regions, respectively., Comment: 30 pages, 21 figures