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Integral properties of the swash zone and averaging. Part 3. Longshore shoreline boundary conditions for wave-averaged nearshore circulation models

The aim of the present work, final of a three-part series, is to analyse in detail flow motions within the swash zone and define suitable shoreline boundary conditions for the longshore flow for wave-averaged circulation models. The analyses of Parts 1 and 2 are extended to cover horizontally two-dimensional flows. An analytical solution for the longshore motion representing the drift velocity of the whole swash zone water mass is found. This is seen to be approximated well by the ratio between the time integral of the longshore momentum flux crossing the swash lower boundary and the swash zone net water volume. Further, a complete set of shoreline boundary conditions, taking into account wave–wave interactions, is obtained on the basis of fully numerical solutions of the nonlinear shallow-water equations. The main focus of the work is to clarify the structure of the shoreline boundary conditions for the longshore flow, but attention has also been paid to their derivation and assessment from the numerical solutions. The latter have been obtained on the basis of a fairly broad range of input wave conditions which, though biased towards those typical of reflective beaches, are believed to cover conditions also typical of moderate dissipative beaches. Two main terms are found to contribute to the longshore drift velocity: (i) a term, proportional to the shallow-water velocity, accounting for short-wave interactions, frictional swash zone forces and continuous forcing due to non-breaking wave nonlinearities and (ii) a drift-type term representing the momentum transfer due to wave breaking.