An expression for the critical shear stress noncohesive sediment is derived from the balance of forces on individual particles at the surface of a bed. The resulting equation, for a given grain size and density, depends on the near‐bed drag force, lift force to drag force ratio, and particle angle of repose. Calculated values of the critical shear stress for uniformly sized sediment correspond closely to those determined from Shields' diagram. The initial motion problem for mixed grain sizes additionally depends on the relative protrusion of the grains into the flow and the particle angle of repose. The latter decreases when the diameter of a moving grain, D, is larger than the length scale of the bed roughness, ks (D/ks > 1), and increases when D/ks < 1, producing a corresponding decrease or increase in critical shear stress. Using the Miller and Byrne experimental relationship between D/ks and particle angle of repose, which is consistent with Shields' definition of initial motion, we obtain results that are in good agreement with the available experimental critical shear stress data for heterogeneous beds.

The wavelength, height, and steepness of ripples formed under oscillatory flows in flume and field studies are reexamined to construct a simple and accurate method of predicting these ripple properties. Ripples with wavelengths proportional to near‐bed wave orbital diameter (orbital ripples), predominant in laboratory experiments, are found to have heights in excess of the thickness of the wave boundary layer. Ripples with wavelengths that are roughly proportional to grain size and nearly independent of orbital diameter (anorbital ripples), which predominate in the field, have heights at least several times smaller than wave boundary layer thickness. Relating wave boundary layer height to the generally more easily estimated wave orbital diameter, a set of expressions are developed for predicting ripple type and geometry based on mean grain size, wave orbital diameter, and estimated anorbital ripple height. This method provides a good characterization of ripple wavelength and steepness for a large set of combined field and flume data.

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A model for the velocity field over a poorly sorted bed is derived herein and applied to flow in steep streams with coarse gravel beds. In such streams, large clasts often are comparable in size to stream depth and act as obstacles to the flow. The effect of these obstacles on a flow is estimated by partitioning total stress, proportional to the depth‐slope product, into a purely fluid component and a form‐drag component associated with flow around the obstacles. An eddy viscosity closure is used, with a length scale dependent on both distance from the boundary and wake dimension. Resulting velocity profiles agree well with profiles measured by Marchand et al. (1984) in nine mountain streams in Colorado. Model runs for a range of conditions reveal that the velocity distribution depends primarily on D84z and flow depth h; D84z is the length of the vertically oriented axis of clasts at the 84th percentile of the grain size distribution. Calculated values of mean velocity, normalized by shear velocity, are well represented by a simple log linear relationship in terms of relative roughness D84/h.

Abstract:A mooring and tripod array was deployed from the fall of 2002 through the spring of 2003 on the Po prodelta to measure sediment transport processes associated with sediment delivered from the Po River. Observations on the prodelta revealed wave-supported gravity flows of high concentration mud suspensions that are dynamically and kinematically similar to those observed on the Eel shelf . Due to the dynamic similarity between the two sites, a simple one-dimensional across-shelf model with the appropriate bottom boundary condition was used to examine fluxes associated with this transport mechanism at both locations. To calculate the sediment concentrations associated with the wave-dominated and wave-current resuspension, a bottom boundary condition using a reference concentration was combined with an "active layer" formulation to limit the amount of sediment in suspension. Whereas the wave-supported gravity flow mechanism dominates the transport on the Eel shelf, on the Po prodelta flux due to this mechanism is equal in magnitude to transport due to wave resuspension and wind-forced mean currents in cross-shore direction. Southward transport due to wave resuspension and wind forced mean currents move an order of magnitude more sediment along-shore than the downslope flux associated wave-supported gravity flows.