Periodic vortex ring cavity formation in an excited submerged jet

When a submerged jet is operated at a sufficiently low cavitation number, {dollar}sigma{dollar}, and is periodically excited (actively or passively) at its source at a particular Strouhal number, S, periodic ring cavities will form. Devices which utilize this phenomenon are useful in achieving increased erosion of materials when the jet is impacted against a boundary, or as generators of sound. Theory is developed to predict the relationship between {dollar}sigma{dollar} and S required to produce periodic ring cavities and to predict the cavity shape and spacing about which the dynamic phenomena take place.; The theory developed approximates the flow field by assuming a uniform translation velocity, and that each cavity cross section shape is steady and may be represented by a three-parameter family of cambered, elliptic-like contours. The flow field is represented in terms of distributions of discrete vortices on the cavity boundaries and unique solutions are obtained which contain two undetermined coefficients, near unity, that must depend on the details of the flow at the generating orifice.; The resulting theory, taking unity for the undetermined coefficients, agrees well with previous data (still photographs) and with new high speed movie data obtained using large jets (1.5 inches diameter) at low speeds (40 to 80 fps) in a variable pressure test loop. The theory shows that the value of S required to obtain structured ring cavities decreases with {dollar}sigma{dollar} and that the cavity cross section becomes increasingly elongated in the streamwise direction as {dollar}sigma{dollar} decreases. For example the theoretical fineness ratio (cross-section length/thickness) varies from 2.2 for ({dollar}sigma{dollar} = 0.3, S = 0.3) to 5.0 for ({dollar}sigma{dollar} = 0.1, S = 0.15) to 10.0 for ({dollar}sigma{dollar} = 0.035, S = 0.08). The natural frequencies and the details of collapse of such elongated cavities must differ significantly from cavities assumed to be circular in cross section.