A semi-empirical formula of beach slope on flat lower platforms

Abstract

The beach slope $\beta$ is a key component characterizing the coastal response to wave forcing. Here we investigate the rapid adaptation of the upper beach slope to a given wave forcing, for the case of a lower flat platform. Such types of morphology are found on coral and rocky reef beaches and low tide terrace environments. The influence of the lower platform on this rapid equilibrium beach state is shown to be significant depending on the breaking wave regime. In particular, the width of the platform and its water level can affect the wave dissipation along the inner surf and thus the wave structure entering the swash. This paper provides a classification of the beach slope equilibrium values as a function of the Dean number on a short time scale (individual wave action), based on both offshore and swash wave conditions. A decreasing trend of the beach slope with increasing offshore Dean number (${\Omega }_0$) is found for ${\Omega }_0\lesssim 2.7$. For ${\Omega }_0\gtrsim 2.7$ it is observed that the beach slope gradient is strongly controlled by the surf zone dissipation and it becomes necessary to define the swash Dean number (${\Omega }_{sw}$) to classify the slope. Finally, a semi-empirical formula for the beach slope evolution in the case of a low tide platform is introduced and tested on two natural low-tide terrace beaches.