A long wave run-up theory is applied to the modelling of wave-induced flow velocities, sediment transport rates and bottom changes in a swash zone. First, the properties of the water tongue motion and the resulting lithodynamic response are analysed theoretically. Next, an attempt is made to run the model for the natural conditions encountered on the southern Baltic Sea coast. The Lagrangian swash velocities are used to determine the Eulerian phase-resolved bed shear stresses with a momentum integral method, after which the motion of sand is described by the use of a two-layer model, comprising bedload and nearbed suspended load. Seabed evolution is then found from the spatial variability of the net sediment transport rates. The results presented are limited to cases of the small-amplitude waves that seem to be responsible for accretion on beaches.
The factors influencing the atmosphere-ocean transfer of mass and momentum, as well as incipient wave breaking and the amount of energy dissipated due to breaking, are discussed in detail. In particular, the influence of directional spreading on the statistics of surface wave slopes and the area of the wind- roughened ocean surface is demonstrated. Theoretical analysis and comparison with the available experimental data show that unimodal directional spreading is not able to reproduce the observed ratio of the cross-wind/up-wind mean square slopes. Better agreement is achieved when bimodal directional spreading, consisting of two wrapped-Gaussian distributions, is applied. The bimodal form suggested by Ewans (1998) is used in the paper. Moreover, the formulae developed here show that the increase in the area due to surface waves is rather small for both regular and irregular waves.
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