Predicting the crest height of a gravel beach

The beach crest is a common morphological feature formed by the deposition of sediment carried up-slope by wave swash. The elevation to which waves can pile gravel is a function of the size and density of the material relative to the hydraulic components of swash velocity, wave frequency and runup height. Two equations ((17) and (21)) that predict the height of the beach crest to the wave forces and the beach material are derived. The first derivation compares the wave force acting to move a stone up the beach face with a weight force acting to hold the stone in place. The second derivation relates the potential energy per unit area of the beach crest to the total wave energy that lifted and deposited the material above a given sea-level datum. As a test of the derived equations, the actual crest height of one natural gravel beach was accurately estimated by both equations derived. Further research and testing on other natural beaches are needed to fully verify Eqs. (17) and (21). A comparison of other equations (Eqs. (2), (3) and (4)) that predict crest height is also made. The poor fit of the other equations are a result of using values for the coefficients that were established in wave tank experiments. Another shortcoming of Eqs. (3) and (4) is that they do not include variables related to the beach material. Hence, they predict that all particle sizes from sand to boulders would be piled to the same elevation by the same wave forcing. Eq. (2) includes a particle size variable but predicts increasingly higher beach crests for larger particles. More realistic results for all three equations (Eqs. (2), (3) and (4)) would be expected with field-tested values for the coefficients, but a range in values for each different beach would be necessary. The advantage of Eqs. (17) and (21) is that equations are not dependent on coefficients whose values come from correlation with other data sets.