Violent breaking wave impacts. Part 2: modelling the effect of air

When an ocean wave breaks against a steep-fronted breakwater, sea wall or a similar marine structure, its impact on the structure can be very violent. This paper describes the theoretical studies that, together with field and laboratory investigations, have been carried out in order to gain a better understanding of the processes involved. The wave's approach towards a structure is modelled with classical irrotational flow to obtain the different types of impact profiles that may or may not lead to air entrapment. The subsequent impact is modelled with a novel compressible-flow model for a homogeneous mixture of incompressible liquid and ideal gas. This enables a numerical description of both trapped air pockets and the propagation of pressure shock waves through the aerated water. An exact Riemann solver is developed to permit a finite-volume solution to the flow model with smallest possible local error. The high pressures measured during wave impacts on a breakwater are reproduced and it is shown that trapped air can be compressed to a pressure of several atmospheres. Pressure shock waves, reflected off nearby surfaces such as the seabed, can lead to pressures comparable with those of the impact. Typical examples of pressure-time histories, force and impulse are presented and discussed in terms of their practical implications. The numerical model proposed is relevant for a variety of flows where air effects are important. Further applications, including extended studies of wave impacts, are discussed.