Sand transport by unbroken water waves under sheet flow conditions

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Abstract
A model of wave‐induced onshore sand transport and resulting topographical changes seaward of the break point on a sloping beach is presented, for the specific case in which the waves are random, normally incident, weakly nonlinear, and relatively long, the bottom boundary layer is fully turbulent, and sand transport occurs as sheet flow. The model consists of the following components: (1) a new empirical expression for sand transport as sheet flow, in which the instantaneous transport rate is directly proportional to the instantaneous bottom shear stress; (2) an expresssion for the mean bottom shear stress, based on a theoretical analysis of the bottom boundary layer; (3) a simple representation of the shoaling wave field, in which the local properties are described by linear long wave theory, the probability density function of the surface displacement is Gaussian, and the waves conserve energy flux as they shoal; and (4) the equation for conservation of sediment mass. Computations based on the model compare favorably with recently reported field measurements of the onshore motion of a long offshore bar.

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