## 4 Numerical Results
### Bubble Dynamics and Noise
The cavitation noise was predicted by modelling each bubble as a point monopole source and its strength was determined by its volume acceleration. The predicted PSD of sound pressure was compared with the measured PSD of sound pressure. There was good agreement between the two results. By comparing the time-history of radius and radial velocity of a single bubble with the corresponding time-variation of sound pressure, it was confirmed that the strong acoustic pressure is generated when a bubble is in the first decay phase. To further investigate the reason for the difference between the predicted and measured cavitation shapes, the Lagrangian computations were repeated by varying the number density of the initial nuclei from freshwater to seawater conditions. The corresponding tip-vortex cavitation shape and radiated acoustic pressure were compared. It was observed that as the number density of nuclei increases from freshwater to seawater, more bubbles develop from the nuclei. Thus, the corresponding acoustic pressure also increases. As more bubbles developed, the cavitation pattern resembled a line-shape observed in the experiment. However, the predicted acoustic spectrum became higher than the measured acoustic spectrum. Given that the strength of point monopole sources assumed in the acoustic computation was proportional to its volumetric acceleration and the total volume of cavitation predicted using the lower nuclei number density was similar to that of the measured tip-vortex cavitation, it was inferred that the simulation using the freshwater condition is best matched to the actual experimental condition. Therefore, the difference between the numerical and experimental results for the tip-vortex cavitation shape was due to the limit of the spherically symmetric bubble dynamics model. Based on the camera-recorded image of the tip-vortex cavitation, it was inferred that the symmetry of the bubbles is broken during the evolution of nuclei into bubbles. Although the current numerical method exhibited difficulty in reproducing the exact shape of tip-vortex cavitation, the predicted cavitation noise matched well with the measured cavitation noise. The additional computations were carried out for the same wing by varying the cavitation number to highlight the ability of the present numerical method to predict the cavitation inception of the wing. The predicted cavitation noise spectrums were compared with the experimental results. There were good agreements between the numerical and experimental results in terms of variation of the spectrum due to the cavitation numbers. The cavitation inception number estimated from the predicted spectrum was the same as that determined from the measured spectrum. Based on these results, the present numerical procedure, utilizing a combination of Eulerian and Lagrangian approaches, can be used as an important tool for analyzing tip-vortex cavitation inception and noise. In future studies, the current numerical methods will be applied to investigate the scale-effects on the CIS of the wings. Furthermore, they will be used to investigate tip-vortex cavitation inception and the noise of underwater propellers. [PERSON] provided the basic idea for this study and the overall numerical strategies. [PERSON] carried out the numerical simulations and worked on the analysis of numerical results. [PERSON] constructed the experimental environment and conducted the experiments. All authors have read and agreed to the published version of the manuscript. This research was funded by Defense Acquisition Program Administration and Agency for Defense Development. This study was carried out as a project of 'Future Submarine Low Noise Propeller Research Laboratory' of KRISO supported by Defense Acquisition Program Administration and Agency for Defense Development. The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.