By the sediment transport rate, also called the sediment discharge, I mean the mass of sedimentary material, both particulate and dissolved, that passes across a given flow-transverse cross section of a given flow in unit time. (Sometimes the sediment transport rate is expressed in terms of weight or in terms of volume rather than in terms of mass.) The flow might be a unidirectional flow in a river or a tidal current, but it might also be the net unidirectional component of a combined flow, even one that is oscillation-dominated. Only in a purely oscillatory flow in which the back-and-forth phases of the flow are exactly symmetrical is there no net transport of sediment. Here we focus on the particulate sediment load of the flow, leaving aside the dissolved load, which is important in its own right but outside the scope of these physics-based notes.
Over the past hundred-plus years, much effort has been devoted to accounting for, or predicting, the sediment transport rate. Numerous procedures, usually involving one or more equations or formulas, have been proposed for prediction of the sediment transport rate. These are commonly called “sediment- discharge formulas”. (The term “formula” here is in some cases a bit misleading: some of the procedures involve the use of reference graphs in addition to mathematical equations.) No single formula or procedure has gained universal acceptance, and only a few have been in wide use. None of them does anywhere near a perfect job in predicting the sediment transport rate—which is understandable, given the complexity of turbulent two-phase sediment- transporting flow and the wider range of joint size–shape frequency distributions that are common in natural sediments. Prediction of the sediment transport rate is one of the most frustrating endeavors in the entire field of sediment dynamics.