The effect of entrained air in violent water wave impacts

The effects of entrained air in cushioning water impact on a wall are estimated by using a flow which has many similarities to the severe flip-through impacts that have been identified for water waves hitting a vertical wall. This is a filling flow which rapidly fills a confined region, such as a crack between blocks, or the space beneath a deck projecting from the coast (Peregrine & Kalliadasis 1996). The main properties of the filling flow are easily calculated, including the high-pressure peak which corresponds to the pressure peak of a flip-through. This work extends the study of filling flows to the case where the filling liquid is an air-water mixture, thus giving explicit results for the reduction of peak pressure due to the compressibility of entrained air. The behaviour of a bubbly liquid subject to substantial pressure changes is considered. Expressions are derived for an air-water mixture treated as a compressible fluid. The reduction in pressure from the incompressible case is found to be large even for relatively small air content, and depends more on the reduction in fluid volume than any other feature of the pressure-density relation. Results are presented in such a way that they may be used to estimate compressibility corrections to both the maximum and background pressures in a flip-through wave impact if corresponding incompressible pressure values are available.