TABLE OF CONTENTS In this section we derive the appropriate averaged boundary conditions to be applied either at a mean air-water interface n = ? or other mean surface such as the base of the surface layer n = b. In either case the assumption of quasi-two-dimensional flow holds as described in section 3 and we introduce a pair of inertial local Cartesian coordinates ( s, n), such that ? is roughly parallel to the surface . Curvilinear, non-inertial, coordinates include further details which obscure the main derivation and follow in Part 3 (Brocchini and Peregrine, 2002).
Although we may define the mean free surface ? for the air-water mixture in terms of the integral of the intermittency factor we find that it is more appropriate to define the boundary conditions at the base of the surface layer. This follows Brocchini and Peregrine (1996) where the boundary conditions for the swash zone flows have been most conveniently obtained at the seaward boundary of the swash zone rather than at any mean shoreline.
General expressions for use at turbulent, discontinuous interfaces are obtained by integrating across the two-phase layer and some comparison is made when possible (e.g. kinematic boundary condition) with the boundary conditions valid for a continuous interface. This integral approach implies that the two-phase surface layer is relatively thin compared with the rest of the flow, and that the surfaces defined by n = constant throughout the layer are sufficiently smooth.
