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The discrete tone radiated from a cavitating tip vortex, known as "vortex singing", was first recognized in 1989, but its sound generation mechanism has remained a mystery for over thirty years. In this letter, by means of the correction for the cavitation bubble dynamics and the dispersion relation of cavity interfacial waves, we found that after the far-end disturbances propagate upstream, the whistling vortex should be triggered by near-end sound sources, the breathing mode waves. Further utilizing the theoretical solutions for singing lines and the potential singing cavitation number with frequency, we accurately identified all available tests for seeking the vortex singing over the past three decades, answering a long-standing perplexity: why such a best whistler is able to appear only within a narrow range of the cavitation number.

The discrete tone radiated from tip vortex cavitation (TVC), known as 'vortex singing', was recognized in 1989, but its triggering remains unclear for over thirty years. In this study, the desinent cavitation number and viscous correction are applied to describe the dynamics of cavitation bubbles and the dispersion relation of cavity interfacial waves. The wavenumber-frequency spectrum of the cavity radius from the experiment in CSSRC indicates that singing waves predominantly consist of the stationary double helical modes (k{\theta} = 2- and -2+) and the breathing mode (k{\theta} = 0-), rather than standing waves as assumed in previous literatures. Moreover, two trigger mechanisms, expressed by two triggering lines, are proposed: the twisted TVC, initially at rest, is driven into motion through the corrected natural frequency (fn) due to the step change of the far-field pressure. Subsequently, the frequency associated with the zero-group-velocity point (fzgv) at k{\theta} = 0- is excited through fi, the frequency at the intersection of dispersion curves at k{\theta} = 0- and -2+, or fj, the frequency at the intersection of dispersion curves at k{\theta} = 0- and 2-, corresponding to two types of the vortex singing triggering. These solutions, without empirical parameters, are validated using singing conditions provided by CSSRC and G.T.H., respectively. Furthermore, the coherence and the cross-power spectral density spectrum indicates a large-scale breathing wave propagating along the singing cavity surface and travelling from downstream to hydrofoil tip, providing us a comprehensive understanding for the triggering of vortex singing.

We conducted a numerical simulation of ventilated supercavitation from a forward-facing cavitator in unsteady flows generated by a gust generator under different gust angles of attack and gust frequencies. The numerical method is validated through the experimental results under specific steady and unsteady conditions. It has been shown that the simulation can capture the degree of cavity shape fluctuation and internal pressure variation in a gust cycle. Specifically, the cavity centerline shows periodic wavelike undulation with a maximum amplitude matching that of the incoming flow perturbation. The cavity internal pressure also fluctuates periodically, causing the corresponding change of difference between internal and external pressure across the closure that leads to the closure mode change in a gust cycle. In addition, the simulation captures the variation of cavity internal flow, particularly the development internal flow boundary layer along the cavitator mounting strut, upon the incoming flow perturbation, correlating with cavity deformation and closure mode variation. With increasing angle of attack, the cavity exhibits augmented wavelike undulation and pressure fluctuation. As the wavelength of the flow perturbation approaches the cavity length with increasing gust frequency, the cavity experiences stronger wavelike undulation and internal pressure fluctuation but reduced cavitation number variation., Comment: 38 pages, 16 figures, submitted to Ocean Engineering