Swash overtopping on plane beaches – Reconciling empirical and theoretical scaling laws using the volume flux

Abstract

Existing empirical and theoretical models for swash overtopping are considered and reconciled by using the positive volume flux of the incident waves and the deficit in freeboard as scaling parameters. This scaling holds for solitary waves, monochromatic waves and random waves. The empirical model of Battjes (1974), the EurOtop model (EurOtop, 2016) and the theoretical model of Peregrine and Williams (2001) can all be written in terms of the positive volume flux with consistent coefficients. This scaling can be rationalised physically by equating the positive volume flux to the volume of fluid displaced by a wavemaker. The empirical exponential vertical scaling in EurOtop is very similar to the empirical vertical scaling identified by Battjes (1974). Here, it is shown that the latter can be rationalised theoretically from a simple ballistic swash model. New experiments on swash overtopping a truncated plane beach are presented for monochromatic and random waves and shown to scale well with these two parameters. Data for equivalent smooth planar beaches from the CLASH database are compared to the new scaling, with good agreement. The influence of beach slope on overtopping has some uncertainty between the theoretical and empirical models, and in the present data, particularly for high deficit in freeboard as the truncation point approaches the still water line. This is likely to be a result of different processes occurring in the surf and swash zones, or over the subaqueous beach face and sub-aerial beach face.