  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.
