Investigation of the resonance frequency of a cavitating vortex

The cavitation pattern of a modern ship propeller is often characterized by a cavitating vortex. This cavitating vortex generates low frequency hull pressure fluctuations which may cause noise and vibration hindrance on board the ship. Analysis of the signals suggests the presence of specific frequency components [1], but detailed investigation is hindered by the complexity of the problem. On the theoretical side, a dispersion relation for waves on cavitating vortices has been developed [2,3] but the applicability of this relation is still unknown. The solution in the limit of small axial wave numbers has been used with some success for comparison with resonance frequencies found in experimental data [4,5] but a motivation for the approach is missing. The paper proposes an alternative procedure in which the method of stationary phase is used to predict resonance frequencies. The approach is validated using measurement data by Maines & Arndt [4] who found resonance frequencies for a cavitating vortex generated by a foil in a cavitation tunnel.