Sand size versus beachface slope — An explanation based on the Constructal Law

Abstract

The relationship between beachface slope and sand grain size has been established based on multiple observations of beach characteristics in many parts of the world. We show that this observational result may be understood in the light of the Constructal Law (Bejan, 1997). A model of wave run-up and run-down along the beachface (swash) was developed to account for superficial flows together with flows through the porous sand bed of average porosity 0.35, the permeability of which may be related to grain diameter and sphericity (0.9 for sand grains) through the Kozeny–Carmán equation. Then, by using the Constructal Law, we minimized the time for completing a swash cycle, under fixed wave height and sand grain diameter. As the result, a relationship involving sand grain size, beachface slope and open ocean wave height has been obtained, and then discussed and validated against experimental data. In addition, this relationship has also been used to illuminate beachface dynamic processes, namely the reshaping of sandy beachfaces in response to changes in wave height. Though the model used in this work may be improved further, the results appear to show, as with other natural systems, that beachface morphing in time may be understood based on a unifying principle — the Constructal Law.