## 4 Numerical Results
### Bubble Dynamics and Noise

Table 4: Signal processing setup for numerical and experiment results. Figure 22: Time histories of (**a**) bubble radius; and (**b**) acoustic pressure due to bubbles for nuclei of initial radius 30 \(\upmu\)m and 40 \(\upmu\)m.  
rebounding phases, especially at the moment of transition from decaying to rebounding. Furthermore, it is evident in Figure 24c that the acoustic pressure generated by the transient acoustic cavitation step is higher than the acoustic pressure generated by a stable acoustic cavitation step, and the acoustic pressure in the decaying and rebounding phase is higher than the acoustic pressure in the growing phase. Generally, the most substantial radius reduction and acoustic pressure occur in the first decaying stage because the maximum energy is released during the first rebound process. Figure 23: Comparison of acoustic pressure between numerical and experimental results; (**a**) power spectral density (PSD); (**b**) band spectrum. Figure 24: (**a**) Bubble radius; (**b**) radius velocity on the arbitrary single bubble; and (**c**) acoustic pressure at a narrow time interval. The Lagrangian computations are repeated to examine the effects of the number density of initial nuclei distribution on the cavitation inception pattern and noise. The number of nuclei in the water is an important parameter for determining the water quality in terms of cavitation inception. Figure 25 shows the distributions of the number concentration density of the initial nuclei used for the computations. The number of total nuclei is varied, but the relative distribution of the number density of nuclei according to their sizes are kept the same as that of seawater shown in Figure 5. The distributed pattern and location are set the same as those shown in Figures 19 and 20, respectively. Figure 26 shows the predicted tip-vortex cavitation shapes and the PSDs of the corresponding acoustic pressure for all the considered cases along with the measured spectrum. As the number density of the initial nuclei increases, more nuclei evolve into cavitation bubbles, and the corresponding acoustic pressure also becomes louder. However, the cavitation shape is more similar to the picture taken via camera, as shown in Figure 21a, as the number density of the nuclei increases to the number density of seawater. Simultaneously, the predicted acoustic spectrum shows a closer agreement with the measured spectrum as the number density of the nuclei approaches that of freshwater. These results are due to the constraints of the bubble dynamics model, which assumes the spherical symmetry for the bubble. It can be inferred from the camera-recorded cavitation shape that the assumed symmetry is broken when the nucleus evolves into a bubble. Bubbles expand into the direction of tip-cavitation and merge with adjacent bubbles. Hence, the predicted cavitation pattern differs from the experimentally visualized pattern when fewer initial nuclei are used. Some studies such as [PERSON] et al. [53] tackled the problem of wing-tip vortex cavitation noise by assuming stable, attached cavity and then a monopolar line source. In terms of the noise generation mechanism, fundamental physics is not different between the two approaches. The present study uses a point monopole source, while the prescribed study uses a line monopole source. Point monopole sources gathering on a line is equivalent to a line monopole source since only volume acceleration of the cavity determines the magnitude of sound source irrespective of its shape. Figure 27 illustrates the situation where the two kinds of sources generate the same sound, although one is intermittent bubble activation, and the other is stable and attached cavity taken from [PERSON] et al. [53].