Initial movement of grains on a stream bed: the effect of relative protrusion

Abstract

Shields (1936) found that the dimensionless shear stress necessary to move a cohesionless grain on a stream bed depended only on the grain Reynolds number. He ignored the degree of exposure of individual grains as a separate parameter. This report describes experiments to measure the dimensionless threshold stress and its dependence on grain protrusion, which was found to be very marked. The threshold stress for grains resting on the top of an otherwise flat bed in a turbulent stream was measured and found to be 0.01 –considerably less than previously-reported values of 0.03–0.06 for beds where all grains were at the same level. It is suggested that the new lower value be used in all turbulent flow situations where the bed is of natural sediments or unlevelled material. An hypothesis is proposed that the conventional Shields diagram implicitly contains variation with protrusion between the two extremes of (i) large grains and large Reynolds numbers, with small relative protrusion, and (ii) small grains, low Reynolds numbers, and protrusion of almost a complete grain diameter. In view of this, the extent of the dip in the Shields plot is explicable in that it represents a transition between two different standards of levelling as well as the transition between laminar and turbulent flow past the grains, the range of which it overlaps considerably.