An energetics bedload model for a plane sloping beach: Local transport

Abstract

Bagnold's energetics‐based sediment transport model for streams is used as a basis for the development of a model for the time‐varying transport of bedload over a plane sloping bed. The sediment transport vector is found to consist of two components: the velocity‐induced transport, directed parallel to the instantaneous velocity vector, and the gravity‐induced transport vector, directed downslope. The model is applied to the case of sediment transport within the surf zone for the separate cases of weak and strong longshore currents, relative to the wave (bore) oscillatory water velocity. The results suggest that Bagnold's oscillatory sediment transport model, which forms the basis for a number of longshore sediment transport models, is only correct for the special case of weak longshore currents and near‐normal incident waves. For an arbitrary strength longshore current v and a local incident wave angle α, the longshore transport rate is found to be proportional to 〈ũ3〉 sin α + 〈ũ2〉v(1 + sin2 α) + v3, where ũ; is the wave‐induced oscillatory water velocity. The model also predicts the onshore‐offshore sediment rate, 〈ix〉. For weak longshore currents and near‐normal incident waves, the predicted equilibrium beach slope is equal to tanϕ〈ũ3〉/〈|ũ;|3〉. Strong longshore currents and or significant local wave angle conditions, however, cause a change in this equilibrium beach slope.