9 Discussion

Following the descriptive and semi-quantitative discussion of Part 1, this paper gives an analytical approach to modelling a strongly disturbed free surface. Full recognition is given to the possibility of a two-phase region. Equations of motion are derived, ab initio, for that region. Although these equations of motion are not new, we need to define notation and we have used an integral approach for the derivation that seems better suited to such discontinuous flows than one based initially on differential equations. In the equation for the turbulent kinetic energy extra work terms appear, both due to the mean pressure and to the mean rate of strain, because of the integral procedure. These contributions, which are identically zero outside the surface layer, show that the air-water mixture within any control volume has some properties like a compressible fluid.

We use the term surface layer to describe the region where both air and water are present, rather than using it for a viscous boundary layer as some authors do. The main aim of the paper is to provide surface boundary conditions that are a simplification of the turbulent air-water mixture making up the surface layer such as occurs at the front and over the top of a spilling breaker. Expressions for boundary conditions are obtained by first taking the usual Reynolds ensemble averages and then integrating across the surface layer. The resulting boundary conditions include a range of new terms. The boundary conditions can best be interpreted as a coupling...