Pulsation of Ventilated Cavities

The problem of pulsating supercavities under artificial ventilation is analytically treated as a resonance problem of a two-dimensional gas-liquid system using a linearized method. A simple kinematical consideration and a dynamical model of the flow lead to solutions for frequency and amplitude of pulsations. The criteria of pulsation is given in terms of a formula relating σ_v and σ. Maximum air carrying capacities of pulsating cavities are also estimated. Most of the formulas involve an undetermined constant which must be estimated by using experimental data. The analytical results are compared with the experimental data obtained at the St. Anthony Falls Hydraulic Laboratory, and in general, good agreement is obtained. It is found that pulsation is possible only for a two-dimensional cavity or a cavity in which a substantial portion of the span can be regarded as two-dimensional. The existence of a free surface is also essential to pulsation. The strong effect of the free surface suggests that pulsation may become an important problem in the open sea only when submergence is relatively small.