Shields parameter

Abstract: In this thesis first a general derivation is given of the 'macro'-equations of mass- and linear-momentum balance that govern the mo'mentum transfer from a Newtonian fluid to rigid particles in a fluid-solid mixture. In particular, attention is paid to a) the attenuation of viscous-momentum transfer from the boundary to the interior of a granular bed subject to a surface flow, b) the drag and lift forces exerted by a turbulent shear flow on particles of the bed surface, and, c) the balance of forces acting on a bed load under uniform-flow conditions. It is shown that filter flow driven by shearing along the boundary of a granular sediment bed exerts a drag force on a layer of only two or three particle diameters within the bed. A drag force on the bulk mass of sediment is only exerted by a pore-pressure gradient. Stability conditions are formulated for a loose granular bed subject to erosive flow, at SHIELDS' grain-movement condition and dUring bed-load transport. 'Macro'-stresses acting along 'wavy' surfaces parallel to the bed are defined for that purpose, and an attenuation factor is introduced for the transmission of turbulent fluid shear from the surface towards the interior of the bed. It is shown that SHIELDS' dimensionless expression for the critical bed shear stress at the threshold of continuous sediment motion, 1/Phi , must reach a constant value for low-shear Reynolds' numbers (Re* < O. 5), as long as there is no cohesion between the particles. It is concluded that the bed load, consisting of particles rolling and saltating over the bed, must reduce the maximum turbulent fluid shear at the bed surface, at sufficiently high bed shear stress, to the critical threshold drag that would lead to the initiation of non-ceasing scour.

Abstract: Data from laboratory flumes and natural streams show that the critical Shields stress for initial sediment motion increases with channel slope, which indicates that particles of the same size are more stable on steeper slopes. This observation is contrary to standard models that predict reduced stability with increasing slope due to the added downstream gravitational force. Processes that might explain this discrepancy are explored using a simple force-balance model, including increased drag from channel walls and bed morphology, variable friction angles, grain emergence, flow aeration, and changes to the local flow velocity and turbulent fluctuations. Surprisingly, increased drag due to changes in bed morphology does not appear to be the cause of the slope dependency because both the magnitude and trend of the critical Shields stress are similar for flume experiments and natural streams, and significant variations in bed morphology in flumes is unlikely. Instead, grain emergence and changes in local flow velocity and turbulent fluctuations seem to be responsible for the slope dependency due to the coincident increase in the ratio of bed-roughness scale to flow depth (i.e., relative roughness). A model for the local velocity within the grain-roughness layer is proposed based on a 1-D eddy viscosity with wake mixing. In addition, the magnitude of near-bed turbulent fluctuations is shown to depend on the depth-averaged flow velocity and the relative roughness. Extension of the model to mixed grain sizes indicates that the coarser fraction becomes increasingly difficult to transport on steeper slopes.

Abstract: [1] We examine relations for hydraulic geometry of alluvial, single-thread gravel bed rivers with definable bankfull geometries. Four baseline data sets determine relations for bankfull geometry, i.e., bankfull depth, bankfull width, and down-channel slope as functions of bankfull discharge and bed surface median sediment size. These relations show a considerable degree of universality. This universality applies not only within the four sets used to determine the forms but also to three independent data sets as well. We study the physical basis for this universality in terms of four relations, the coefficients and exponents of which can be back calculated from the data: (1) a Manning-Strickler-type relation for channel resistance, (2) a channel-forming relation expressed in terms of the ratio of bankfull Shields number to critical Shields number, (3) a relation for critical Shields number as a function of dimensionless discharge, and (4) a “gravel yield” relation specifying the (estimated) gravel transport rate at bankfull flow as a function of bankfull discharge and gravel size. We use these underlying relations to explore why the dimensionless bankfull relations are only quasi-universal and to quantify the degree to which deviation from universality can be expected. The analysis presented here represents an alternative to extremal formulations to predict hydraulic geometry.