Sediment entrainment under fully developed waves as a function of water depth, boundary layer thickness, bottom slope and roughness

Many sediment entrainment equations for oscillatory waves are based on the linear (Airy) theory for deep water, but at the depth where such waves begin to transport sediments they commonly have trochoidal or cnoidal (non-linear) forms. These changes in the wave profile, together with the fact that it is displaced upward with respect to the still water level (SWL), have a profound influence on the hydrodynamics. A method is presented to determine the thickness of the boundary layer from the wave profile, which can be used to calculate the boundary velocity under the wave crest and trough, respectively, in any water depth. The critical boundary velocity can be determined from a published procedure based on laboratory experiments that takes account of the sediment and water properties as well as the wave period. An adjustment is made for the bottom slope and roughness, so that differential land- or seaward sediment entrainment can be predicted for any defined wave cycle. The results explain why sediments are normally transported landward under fair weather conditions and seaward during storms.