Variable Shields number model for river bankfull geometry: bankfull shear velocity is viscosity-dependent but grain size-independent

The bankfull geometry of alluvial rivers is thought to be controlled by water and sediment supply, and characteristic sediment size. Here we demonstrate a novel finding: when bankfull shear velocity and bankfull depth are correlated against bed material grain size and bed slope, they are to first order independent of grain size and dependent on water viscosity. We demonstrate this using a similarity collapse for bankfull Shields number as a function of slope and grain size, obtained with data for 230 river reaches ranging from silt-bed to cobble-bed. Our analysis shows that bankfull Shields number increases with slope to about the half power. We show that the new relation for bankfull Shields number provides more realistic predictions for the downstream variation of bankfull characteristics of rivers than a previously used assumption of constant bankfull Shields number.