Bubbles and waves description of self-aerated spillway flow

The "continuum" description of self-aerated spillway flow has adequately served to describe spillway bulking, but encounters difficulties when applied to other physical phenomena, such as cavitation and gas transfer. The continuum description is adapted to separate air being transported by the flow as bubbles ("entrained" air), and air transported with the flow in the roughness or waves of the water surface ("entrapped" air). Results from flume experiments on aerated flow are used to develop an analysis procedure and mathematical description of entrained and entrapped air for flow along a spillway face. Entrapped air is found to be constant at a void ratio, with a vertical distribution analogous to the "intermittent" region of a turbulent boundary layer. Entrained air gradually increases to a maximum value depending on slope. Cain's dimensionless distance is used to collapse entrained air data from several unit discharges with the same slope to a single relationship. The analysis procedure and dimensionless parameter provide a means of analyzing a large store of additional literature data. Observations from a full-scale spillway provide verification of the procedure.