Analysis of inertial waves on inviscid cavitating vortices in relation to low-frequency radiated noise

The dispersion relation of inertial waves on inviscid cavitating vortices ('Kelvin waves') is reconsidered and extended to include the influence of a convection velocity and compressibility for acoustic analysis. Different aspects of the dispersion relation are discussed with emphasis on the variation of the frequency, the phase speed and the group speed for low frequency variations of the first three modes. A zero group speed criterion is used to derive a formulation for the resonance frequencies of the breathing mode. The obtained relation between the frequency and the cavitation number shows a reasonable correlation with experimental data. In addition some aspects are discussed of the radiated noise of cavitating vortex deformations without collapse.