  In the study of ocean wave impact on structures, one often uses Froude
scaling since the dominant force is gravity. However the presence of trapped or
entrained air in the water can significantly modify wave impacts. When air is
entrained in water in the form of small bubbles, the acoustic properties in the
water change dramatically and for example the speed of sound in the mixture is
much smaller than in pure water, and even smaller than in pure air. While some
work has been done to study small-amplitude disturbances in such mixtures,
little work has been done on large disturbances in air-water mixtures. We
propose a basic two-fluid model in which both fluids share the same velocities.
It is shown that this model can successfully mimic water wave impacts on
coastal structures. Even though this is a model without interface, waves can
occur. Their dispersion relation is discussed and the formal limit of pure
phases (interfacial waves) is considered. The governing equations are
discretized by a second-order finite volume method. Numerical results are
presented. It is shown that this basic model can be used to study violent
aerated flows, especially by providing fast qualitative estimates.
