Jonathan M. Nelson

Role of Near-Bed Turbulence Structure in Bed Load Transport and Bed Form Mechanics

The interactions between turbulence events and sediment motions during bed load transport were studied by means of laser-Doppler velocimetry and high-speed cinematography. Sweeps (u′ > 0, w′ 0 w′ > 0) which contribute negatively to the bed shear stress and are relatively rare, individually move as much sediment as sweeps of comparable magnitude and duration, however, and much more than bursts (u′ 0) and inward interactions (u′ < 0, w′ < 0). When the magnitude of the outward interactions increases relative to the other events, therefore, the sediment flux increases even though the bed shear stress decreases. Thus, although bed shear stress can be used to estimate bed load transport by flows with well-developed boundary layers, in which the flow is steady and uniform and the turbulence statistics all scale with the shear velocity, it is not accurate for flows with developing boundary layers, such as those over sufficiently nonuniform topography or roughness, in which significant spatial variations in the magnitudes and durations of the sweeps, bursts, outward interactions, and inward interactions occur. These variations produce significant peaks in bed load transport downstream of separation points, thus supporting the hypothesis that flow separation plays a significant role in the development of bed forms.

Mean flow and turbulence fields over two-dimensional bed forms

Detailed laser-Doppler velocity and Reynolds stress measurements over fixed two-dimensional bed forms are used to investigate the coupling between the mean flow and turbulence and to examine effects that play a role in producing the bed form instability and finite amplitude stability. The coupling between the mean flow and the turbulence is explored in both a spatially averaged sense, by determining the structure of spatially averaged velocity and Reynolds stress profiles, and a local sense, through computation of eddy viscosities and length scales. The measurements show that there is significant interaction between the internal boundary layer and the overlying wake turbulence produced by separation at the bed form crest. The interaction produces relatively low correlation coefficients in the internal boundary layer, which suggests that using local bottom stress to predict bed load flux may not only be erroneous, it may also disregard the essence of the bed form instability mechanism. The measurements also indicate that topographically induced acceleration over the bed form stoss slope has a more significant effect in damping the turbulence over bed forms than was previously supposed, which is hypothesized to play a role in the stabilization of fully developed bed forms.

Variability of bed mobility in natural, gravel-bed channels and adjustments to sediment load at local and reach scales

Local variations in boundary shear stress acting on bed-surface particles control patterns of bed load transport and channel evolution during varying stream discharges. At the reach scale a channel adjusts to imposed water and sediment supply through mutual interactions among channel form, local grain size, and local flow dynamics that govern bed mobility. In order to explore these adjustments, we used a numerical flow model to examine relations between model-predicted local boundary shear stress (тj( and measured surface particle size (D50) at bank-full discharge in six gravel-bed, alternate-bar channels with widely differing annual sediment yields. Values of тj and D50 were poorly correlated such that small areas conveyed large proportions of the total bed load, especially in sediment-poor channels with low mobility. Sediment-rich channels had greater areas of full mobility; sediment-poor channels had greater areas of partial mobility; and both types had significant areas that were essentially immobile. Two reach-mean mobility parameters (Shields stress and Q*) correlated reasonably well with sediment supply. Values which can be practicably obtained from carefully measured mean hydraulic variables and particle size would provide first-order assessments of bed mobility that would broadly distinguish the channels in this study according to their sediment yield and bed mobility.

Turbulence structure over two‐dimensional bed forms: Implications for sediment transport

Turbulence measurements from the flow over two-dimensional fixed dune shapes are presented along with analysis and discussion of the ramifications of the observations for transport of sediment as bed load over bed forms. The spatial structure of the local transport rate determines the shape and stability of bed forms such as ripples and dunes, and the transport of sediment is a highly nonlinear process that is profoundly affected by the statistics of the temporal fluctuations in the near-bed flow field. The measurements presented herein show strong spatial evolution of the joint probability distribution of the streamwise and bednormal fluctuating velocity components. Unlike measurements in uniform boundary layers, these distributions and the higher moments of the velocity do not scale with the local shear velocity, indicating that it is probably inappropriate to use the shear stress to characterize the sediment flux. This conclusion is supported by observations of sediment flux over a dune.

UNIDIRECTIONAL FLOW OVER ASYMMETRIC AND SYMMETRIC RIPPLES

Detailed measurements of velocity and turbulence over fixed sets of two-dimensional asymmetric and symmetric ripples were collected in a flume equipped with a laser-Doppler velocimeter. The measured velocity profiles show a region of strong wake influence extending 2–3 bedform heights above the bed and an outer, spatially uniform flow that has adjusted to the hydrodynamic roughness of the ripples. The measured velocities over ripples, when compared to measurements of flow over larger-scale dunes of a similar geometry made by Nelson and Smith (1989), differ in two major respects: the velocity gradients are significantly larger in the outer region of the flow, and the velocity profiles exhibit no sharp inflection at the top of the lowest wake. A model for flow over bedforms that had provided excellent agreement with the dune measurements is modified herein in a physically reasonable manner to represent better the observed flow over ripples. The predictions of the modified model compare well with the velocity measurements made over sets of asymmetric and symmetric ripples in a unidirectional flow when the appropriate drag coefficients for the two bed geometries are used. Drag coefficients deduced from the measurements suggest a possible dependence on relative depth as well as ripple geometry. Hydrodynamic ripple roughnesses determined from the measured and calculated profiles have values of the same order as estimates made using several existing expressions for the roughness of bedforms and regular roughness arrays. However, the measurements and calculations also indicate that bottom roughness depends on more than the ripple height times ripple steepness length scale used in these formulations.

Spatially averaged flow over a wavy boundary revisited

Vertical profiles of streamwise velocity measured over bed forms are commonly used to deduce boundary shear stress for the purpose of estimating sediment transport. These profiles may be derived locally or from some sort of spatial average. Arguments for using the latter procedure are based on the assumption that spatial averaging of the momentum equation effectively removes local accelerations from the problem. Using analogies based on steady, uniform flows, it has been argued that the spatially averaged velocity profiles are approximately logarithmic and can be used to infer values of boundary shear stress. This technique of using logarithmic profiles is investigated using detailed laboratory measurements of flow structure and boundary shear stress over fixed two-dimensional bed forms. Spatial averages over the length of the bed form of mean velocity measurements at constant distances from the mean bed elevation yield vertical profiles that are highly logarithmic even though the effect of the bottom topography is observed throughout the water column. However, logarithmic fits of these averaged profiles do not yield accurate estimates of the measured total boundary shear stress.

Interparticle collision of natural sediment grains in water

Elastohydrodynamic theory and measurements of particle impacts on an inclined glass plane in water are used to investigate the mechanics of interparticle collisions in sediment-transporting flows. A collision Stokes number is proposed as a measure of the momentum of an interparticle collision versus the viscous pressure force in the interstitial gap between colliding particles. The viscous pressure force opposes motion of the particles on approach and rebound. A Stokes number of between 39 and 105 is estimated as the critical range below which particle impacts are completely viscously damped and above which impacts are partially elastic. The critical Stokes number is shown to roughly coincide with the Bagnold number transition between macroviscous and grain inertial debris flows and the transition between damped and partially elastic bed load transport saltation impacts. The nonspherical nature of natural particles significantly alters the motion of the center of mass after a partially elastic collision. The normal to the point of contact between the particles does not necessarily go through the center of mass. Thus normal rebound of the center of mass may not occur. A model of particle motion after rebound for particles of arbitrary shape, conserving both linear and angular momentum, is proposed.

The initial instability and finite-amplitude stability of alternate bars in straight channels

Abstract The initial instability and fully developed stability of alternate bars in straight channels are investigated using linearized and nonlinear analyses. The fundamental instability leading to these features is identified through a linear stability analysis of the equations governing the flow and sediment transport fields. This instability is explained in terms of topographically induced steering of the flow and the associated pattern of erosion and deposition on the bed. While the linear theory is useful for examining the instability mechanism, this approach is shown to yield relatively little information about well-developed alternate bars and, specifically, the linear analysis is shown to yield poor predictions of the fully developed bar wavelength. A fully nonlinear approach is presented that permits computation of the evolution of these bed features from an initial perturbation to their fully developed morphology. This analysis indicates that there is typically substantial elongation of the bar wavelength during the evolution process, a result that is consistent with observations of bar development in flumes and natural channels. The nonlinear approach demonstrates that the eventual stability of these features is a result of the interplay between topographic steering effects, secondary flow production as a result of streamline curvature, and gravitationally induced modifications of sediment fluxes over a sloping bed.

Colorado River sediment transport 2. Systematic bed-elevation and grain-size effects of sand supply limitation

The Colorado River in Marble and Grand Canyons displays evidence of annual supply limitation with respect to sand both prior to (Topping et al., this issue) and after the closure of Glen Canyon Dam in 1963. Systematic changes in bed elevation and systematic coupled changes in suspended-sand concentration and grain size result from this supply limitation. During floods, sand supply limitation either causes or modifies a lag between the time of maximum discharge and the time of either maximum or minimum (depending on reach geometry) bed elevation. If, at a cross section where the bed aggrades with increasing flow, the maximum bed elevation is observed to lead the peak or the receding limb of a flood, then this observed response of the bed is due to sand supply limitation. Sand supply limitation also leads to the systematic evolution of sand grain size (both on the bed and in suspension) in the Colorado River. Sand input during a tributary flood travels down the Colorado River as an elongating sediment wave, with the finest sizes (because of their lower settling velocities) traveling the fastest. As the fine front of a sediment wave arrives at a given location, the bed fines and suspended-sand concentrations increase in response to the enhanced upstream supply of finer sand. Then, as the front of the sediment wave passes that location, the bed is winnowed and suspended-sand concentrations decrease in response to the depletion of the upstream supply of finer sand. The grain-size effects of depletion of the upstream sand supply are most obvious during periods of higher dam releases (e.g., the 1996 flood experiment and the 1997 test flow). Because of substantial changes in the grain-size distribution of the bed, stable relationships between the discharge of water and sand-transport rates (i.e., stable sand rating curves) are precluded. Sand budgets in a supply-limited river like the Colorado River can only be constructed through inclusion of the physical processes that couple changes in bed-sediment grain size to changes in sand-transport rates. In some rivers the upstream supply of sediment is in equi- librium with the upstream supply of water, whereas in others, the upstream supply of sediment is decoupled, either com- pletely or partially, from the upstream supply of water. In the first type of river, changes in sediment transport are controlled by changes in the discharge of water, whereas in the second (and perhaps more common) type of river, changes in sedi- ment transport are also coupled to changes in sediment grain size. In this paper we investigate the systematic changes in bed elevation, sediment transport, and sediment grain size that occur in response to changes in the upstream supply of sand in a river with an intermittent limited supply of sand, specifically the Colorado River in Marble and Grand Canyons (Figure 1). To develop an intuitive understanding of the linkage be- tween sediment grain size and the upstream supply of sediment in a river, it is informative to first examine sediment-transport

Relation of inversely graded deposits to suspended-sediment grain-size evolution during the 1996 flood experiment in Grand Canyon

Before Glen Canyon Dam was completed upstream from Grand Canyon, floods scoured sand from the channel bed and deposited sand on bars within recirculating eddies. After completion of Glen Canyon Dam in 1963, peak discharge of the mean annual floods dropped from about 2600 to 900 m 3 /s, and 85% of the sediment supply was eliminated. Under the postdam flow regime, sand bars in eddies have degraded. In an experiment to study, in part, the effects of floods in rebuilding these bars, a controlled flood was released from Glen Canyon Dam in late March and early April 1996. Although fluvial sequences characteristically fine upward, the deposits of the experimental flood systematically coarsen upward. Measurements of suspendedsediment concentration and grain size and of bed-material grain size suggest that the upward coarsening results from the channel becoming relatively depleted of fine-grained sediment during the seven days of the high-flow experiment. Predam flood beds of the Colorado River also coarsen upward, indicating that supply-limitation and grain-size evolution are natural processes that do not require the presence of a dam.