Cross‐shore suspended sand and bed load transport on beaches

Simple formulas are developed to predict the time‐averaged rates of cross‐shore suspended sand and bed load transport. The net suspended sand transport rate is expressed as the product of the depth‐averaged current and the suspended sediment volume per unit bottom area with a reduction factor that accounts for the correlation between the time‐varying fluid velocity and sediment concentration. The net bed load transport rate under nonlinear waves is assumed to be onshore and proportional to σ U 3 where σ U is the standard deviation of the horizontal velocity. The probabilities of sediment movement and suspension are introduced to account for the initiation of sediment movement and suspension. Simple functions are proposed to account for the effects of a steep bottom slope on the bed load and suspended sediment transport rates. The proposed formulas are found to be in agreement with three data sets within a factor of about 2. The proposed formulas are shown to be consistent with existing simple formulas. The formulas are incorporated into a time‐averaged wave model and the continuity equation of bottom sediment to predict the beach profile evolution. The numerical model is compared with seven small‐scale tests including berm erosion tests and seven large‐scale tests including dune erosion tests. The numerical model predicts the overall beach profile evolution including the berm and dune erosion but does not always predict the fairly subtle profile changes including bar migration accurately.