A rational sediment transport scaling relation based on dimensionless stream power

Abstract

Abstract The concept of stream channel grade – according to which a stream channel reach will adjust its gradient, S , in order to transport the imposed sediment load having magnitude Q b and characteristic grain size D b , with the available discharge Q (Mackin, 1948 , Geological Society of America Bulletin 59 : 463–512; Lane, 1955 , American Society of Civil Engineers, Proceedings 81 : 1–17) is one of the most influential ideas in fluvial geomorphology. Herein, we derive a scaling relation that describes how externally imposed changes in either Q b or Q can be accommodated by changes in the channel configuration, described by the energy gradient, mean flow depth, characteristic grain size and a parameter describing the effect of bed surface structures on grain entrainment. One version of this scaling relation is based on the dimensionless bed material transport parameter ( W *) presented by Parker and Klingeman ( 1982 , Water Resources Research 18 : 1409–1423). An equivalent version is based on a new dimensionless transport parameter ( E *) using dimensionless unit stream power. This version is nearly identical to the relation based on W *, except that it is independent of flow resistance. Both versions of the scaling relation are directly comparable to Lane's original relation. In order to generate this stream power‐based scaling relation, we derived an empirical transport function relation relating E * to dimensionless stream power using data from a wide range of stable, bed load‐dominated channels: the form of that transport function is based on the understanding that, while grain entrainment is related to the forces acting on the bed (described by dimensionless shear stress), sediment transport rate is related to the transfer of momentum from the fluid to the bed material (described by dimensionless stream power). Copyright © 2010 John Wiley & Sons, Ltd.