Laboratory observations and computational results for the response of bedform fields to rapid variations in discharge are compared and discussed. The simple case considered here begins with a relatively low discharge over a flat bed on which bedforms are initiated, followed by a short high-flow period with double the original discharge, during which the morphology of the bedforms adjusts, followed in turn by a relatively long period of the original low discharge. For the grain size and hydraulic conditions selected, the Froude number remains subcritical during the experiment, and sediment moves predominantly as bedload. Observations show rapid development of quasi-two-dimensional bedforms during the initial period of low flow with increasing wavelength and height over the initial low-flow period. When the flow increases, the bedforms rapidly increase in wavelength and height, as expected from other empirical results. When the flow decreases back to the original discharge, the height of the bedforms quickly decreases in response, but the wavelength decreases much more slowly. Computational results using an unsteady two-dimensional flow model coupled to a disequilibrium bedload transport model for the same conditions simulate the formation and initial growth of the bedforms fairly accurately and also predict an increase in dimensions during the high-flow period. However, the computational model predicts a much slower rate of wavelength increase, and also performs less accurately during the final low-flow period, where the wavelength remains essentially constant, rather than decreasing. In addition, the numerical results show less variability in bedform wavelength and height than the measured values; the bedform shape is also somewhat different. Based on observations, these discrepancies may result from the simplified model for sediment particle step lengths used in the computational approach. Experiments show that the particle step length varies spatially and temporally over the bedforms during the evolution process. Assuming a constant value for the step length neglects the role of flow alterations in the bedload sediment-transport process, which appears to result in predicted bedform wavelength changes smaller than those observed. However, observations also suggest that three-dimensional effects play at least some role in the decrease of bedform wavelength, so incorporating better models for particle hop lengths alone may not be sufficient to improve model predictions. Published in 2011. This article is a US Government work and is in the public domain in the USA.

Incidents of chute cutoff are pervasive along many meandering rivers worldwide, but the process is seldom incorporated into theoretical analyses of planform evolution, partly due to the paucity of observations describing its physical controls. Here, we describe a mechanism of chute cutoff that may be prevalent along large meandering rivers with uniform floodplain topography. The mechanism occurs independently of sudden changes in conveyance capacity, such as those caused by natural dams, and instead, it is initiated during a flood by the incision of an embayment. The embayment is typically located almost a channel width upstream of the entrance to the meander that undergoes cutoff, and subsequent floods extend the embayment downstream until a chute is formed. Using sequences of historical aerial photos of the Sacramento River in California, USA, we found that embayments formed where channel curvature was greatest, or where the channel most tightly curved away from the downstream flow path. Embayments formed only within those portions of the floodplain that were lightly vegetated by grasses or crops. We develop a simple physical model that describes the environmental conditions that can lead to embayment formation. The model considers the role of floodplain vegetation in preventing chute incision and in part explains why chute cutoff is prevalent along some meandering rivers but not others.

Relatively little is known about sediment suspension over dunes. Using spatial averages (at constant distance from the local bed) of the mean flow and turbulent stresses over dunes in a river, Smith & McLean (1977) postulated an eddy diffusivity profile for suspended sediment that consisted of two linear segments. This resulted in concentration profiles with two Rouse-like segments. More recently, based on spatial averages of velocity and Reynolds stress along horizontal planes above fixed-bed dune shapes, the eddy viscosity (diffusivity) profile has been found to have a more complex shape that yields a more exponential-type concentration profile near the bed. Measurements of flow and echo strength over triangular dune shapes in the laboratory using an acoustic Doppler profiling system, spatially averaged in a similar way, show that velocity and concentration profiles indeed reflect this more complex eddy diffusivity. Furthermore, the measurements suggest that spatial correlations between vertical velocity and suspended sediment contribute to the upward flux of sediment.

Spatially averaged profiles of time averaged velocity, using integrals over thin horizontal slabs (Cartesian double average), are employed in characterizing the flow over fixed dune shapes. For comparison the spatial averaging method of Smith and McLean (1977) that averages along lines at constant distance from the local bed elevation is also investigated. The Cartesian double averaged profiles of the inverse of the velocity shear are nearly constant below the crest elevation, but increase rapidly above the crest level. This results in velocity profiles that increase linearly with distance from the bed below the crest. Above the crest it can be argued that the velocity increases logarithmically, but a power law profile can also be argued. Spatially averaged eddy viscosity profiles are calculated by multiplying the average Reynolds stress by the inverse shear. The resulting profile is more complex than the uniform flow counterpart.

Spatial averaging of the Reynolds-averaged Navier-Stokes equations gives the double-averaged Navier-Stokes equations, for which boundary drag appears naturally and explicitly in momentum Conservation equations. Increasing use of the double-averaged equations, e.g., for relating flows to three-dimensional bed toughness, for evaluation of profiles of flow stresses and velocities in ecologically significant regions below roughness tops, and for modeling purposes, requires parameterization of boundary drag at subelement scales. Based on seven flows over repeated square-rib roughness and ten flows over repeated fixed simulated sand waves, with measured velocities and bed pressures, expressions for form-drag coefficient C-D = f (elevation below roughness top, relative roughness submergence, roughness steepness) are obtained for each of the two-dimensional roughness types. Using these equations, form drag variation with elevation below roughness can be calculated using either the double average of the square of local velocity (preferred based Oil conceptual considerations, trends in coefficient prediction, and also overall drag prediction) or the squared local double-averaged velocity, the roughness area being normal to the flow in each case. Integration of subelement drag given by these expressions is shown to Give form-drag coefficient magnitudes and trends for complete individual elements comparable to those obtained by other authors based on measurements or numerical simulations. The ranges Of roughness steepness and relative roughness submergence upon which the present equations have been derived need to be noted in consideration of application of the equations. In addition, effective application of the expressions is limited in regions of strongly negative double-averaged velocity. Further work remains to determine drag parameterization for alternative roughness geometries.

The goal of this paper is to discuss the spatial averaging concept in environmental hydraulics and develop it further by considering transport equations for fluid momentum, passive substances, and suspended sediments. The averaging theorems, the double-averaged (in time and in space) fluid momentum equation, and advection-diffusion equations for a passive substance and suspended sediments are introduced and their limitations and applications for modeling rough-bed flows, experimental design, and data interpretation are discussed. The suggested equations differ from those considered in terrestrial canopy aerodynamics and porous media hydrodynamics by accounting for roughness mobility, change in roughness density in space and time, and particle settling effects for the case of suspended sediments. We show that the form of the double-averaged equations may depend on the type of decomposition of flow variables and that this difference may have important implications for modeling. We also show that the suggested methodology offers better definitions for hydraulic characteristics, variables, and parameters such as flow uniformity, flow two dimensionality, and bed shear stress.

A series of experiments was undertaken to assess fully rough turbulent subcritical flow over two-dimensional transverse repeated-rib roughness of varying spacing lambda/h = I - 16 (roughness spacing/height ratio), with h/H = 0.09 (roughness height/flow depth). Each of the 11 experiments involved centerline measurements of three-dimensional velocity vectors, water surface profiles, and bed pressures and forces. The structure of flow over rib roughness consists of a pair of principal vortices of opposite sign set up by the ribs. These vortices are superimposed on an overall double- (time and space)-averaged velocity profile that is (quasi-) logarithmic above roughness tops, and that below roughness tops changes with increasing rib spacing from exponential (lambda/h < 10) to linear (lambda/h >= 10) to logarithmic (lambda/h >> 10). The measured double-averaged velocity profiles are parameterized herein, and double-averaged Reynolds and form-induced stress profiles and trends are also identified. Maximum drag due to wall roughness is found to occur for lambda/h approximate to 8. The experimentally determined momentum balance, including effects of secondary currents and flow acceleration, is found to agree well with theoretical expectations. It is shown that the knowledge of the effects of form-induced stresses, secondary currents, and flow nonuniformity may be particularly important for describing and modeling flows over roughness elements.

We address some unsolved methodological issues in modeling of natural rough‐bed flows by critically examining existing approaches that parameterize rough‐bed flows. These often utilize loosely defined variables. Here we suggest that double‐averaging (in time and in a volume occupying a thin slab in a plane parallel to the mean bed) provides a rigorous, straightforward alternative that can aid in the parameterization process. We further present two examples: two‐dimensional bed form and gravel bed flows. We argue that the double‐averaging approach based on momentum equations should serve as a better methodological basis for modeling, phenomenological developments, and parameterizations. These equations explicitly include drag terms and form‐induced momentum fluxes due to spatial heterogeneity of the time‐averaged flow in the near‐bed region. They also provide a solid basis for better definitions of basic flow variables including the shear stress partitioning into turbulent and form‐induced momentum fluxes, skin friction, and pressure (form) drag. We show that for a range of rough‐bed flows the vertical distribution of the double‐averaged velocity consists of two distinct regions: (1) a linear region below roughness tops, and (2) a logarithmic region above them.

Experiments utilizing two-dimensional fixed dune profiles and varying flow depth (dune regime flows) highlight the equilibrium (self-similar) nature of the near-bed boundary layer over developing dunes with flow separation in the dune lee. The negligible variation in roughness layer (comprising the interfacial and form-induced layers) flow structure for developing dunes was confirmed in terms of spatial fields of time-averaged velocities and stresses; and vertical distributions of: (a) double-averaged (in time and space) longitudinal velocity, (b) double-averaged normal stresses, and (c) the components of the momentum balance for the flow. The finding of an equilibrium nature for the near-bed flow over developing dunes is significant in its centrality to understanding the feedback loop between flow, bed morphology, and sediment transport that controls erodible-bed development. Further research is required into the form of the distribution of double-averaged velocity in the form-induced layer above roughness tops, and also to complete generalization for varying dune steepness of the universal expression for double-averaged longitudinal velocity (varying linearly with elevation) determined herein for the interfacial layer (below roughness tops). Work is presently focusing on the additional effects on flow structure due to sediment transport and three-dimensional flow and bed morphology, although it is expected that the equilibrium boundary layer flow structure patterns identified herein will still be evident for these more complex systems.

Bedforms such as ripples and dunes represent bottom features that exist at in least quasi- equilibrium with the overlying flow. Because of flow separation that is typically associated with these features, the flow over them is highly complex. Sediment transport is highly dependent on the nature of the overlying turbulence field. The turbulence is characteristic of neither wakes nor of classic boundary layers and its structure is spatially variable. Topography-induced acceleration plays a critical role in the nature of the turbulence field. Measurements of mean flow and turbulence are presented here for separated flow over a range of bed slopes simulating bedforms of different steepness ratios. Steep slopes are found to significantly reduce the overlying turbulence. Future experiments to assess the effects of slope on sediment flux are described.

Several models for the vertical distribution of the double-averaged (in time and in the plane parallel to the mean bed) longitudinal velocity in the flow region between roughness troughs and roughness tops are suggested. We found that the same model for velocity distribution may be applicable to a range of flow conditions and roughness types, which share some common features. The suggested models for velocity distribution in the near-bed region are: (1) Constant velocity; (2) exponential velocity distribution; and (3) linear velocity distribution. The measured velocity distributions may be approximated by a single model or by a combination of models depending on roughness geometry and flow conditions. The validity of these models for velocity distribution is supported by laboratory data.

Scouring of the seabed around man-made structures is a perplexing problem for coastal and ocean engineers. Even robust structures can experience damage, or possibly failure, brought about by scour around the foundation. Ignoring potential consequences of scour and failing to provide adequate scour protection are unacceptable engineering practices. On the other hand, scour is very specific to structure type and hydrodynamic environment. Thus, it may be difficult to anticipate where scour might occur and whether the scour will put the structure at risk. Ideally, the engineer would like to provide scour protection only where needed to minimize cost, but our understanding of scour processes does not allow this option for all situations. It has long been recognized that scour occurs whenever the hydrodynamic forces of moving water exceed the resistive forces holding sediment particles at rest. However, developing theoretical relationships between fluid and sediment is still a challenge for all but the most simple cases. Quantifying scour at structures in terms of predictable hydrodynamic parameters remains the forte of experimentalists who observe the scouring action, recognize the dominant physical processes, and establish empirical engineering relationships for predicting scour. Anyone with even a casual interest in scour caused by waves and currents will have encountered the work of Mutlu Sumer and Jorgen Fredsoe. Over the past 20–25 years, these two industrious collaborators have studied scour phenomena and developed practical engineering guidance. Their new book, The Mechanics of Scour in the Marine Environment, collects their research findings, and the works of others, into a well organized and convenient volume that is part of the Advanced Series on Ocean Engineering published by World Scientific. It appears that the book is available only in hardback and not softback, which is a departure from previous volumes in this series. The bulk of material in this 500 plus page book pertains to scour of noncohesive sediment, but the authors have included available information and references related to cohesive sediment scour for specific situations. Throughout the book, the authors emphasize the need to understand the hydrodynamic processes producing scour as the most important step toward scour prediction. After introducing basic concepts ~Chapter 1!, the book’s remaining nine chapters cover pipeline scour ~Chapter 2!; scour at piles ~Chapters 3–6!; scour around coastal structures ~Chapters 7–8!; ship-propeller scour ~Chapter 9!; and the impact of liquefaction on pipelines and armor blocks ~Chapter 10!. Each chapter ends with references to literature cited within the chapter. An appendix provides a handy summary of key equations from linear wave theory, and the subject and author indexes round out the book. The list of symbols is placed directly after the table of contents. Well-drawn figures illustrating various scour concepts

Dunes formed in response to fluid flow exert a total boundary stress on the fluid that is made up of form drag and skin friction, the latter of which is generally considered important for predicting sediment transport and dune evolution. Previous research has used various methods to estimate the total stress and its subcomponents, with recent work suggesting the application of a spatial average to the equations of motion. A complete, three‐dimensional (3‐D) form of this analysis is derived and applied to recent measurements of turbulent open‐channel flow over 3‐D dunes. Spatial averages of Reynolds shear stresses over 3‐D dunes cannot be used to predict total boundary shear stress. However, estimations of total boundary shear stress from the spatially averaged equations of motion agree with not only the sum of form drag and skin friction but also the direct measurements of average free surface slope. Form‐induced stresses from secondary circulations augment the relatively low Reynolds shear stresses over the 3‐D dunes. These low turbulence levels have ramifications for sediment transport predictions, in that use of the total boundary shear stress in prediction of sediment transport over 3‐D dunes must account for these low turbulence levels so as not to overpredict transport rates.

The design of a straight benthic flow-through flume for in situ studies of cohesive sediment dynamics is described including the flume structure and probes installed for routine measurements of suspended sediments and flow velocity. The flume was calibrated for two roughness types covering the range of possible cohesive bed roughnesses. The calibration included a set of three-dimensional velocity measurements using acoustic Doppler velocimeter. These measurements were used to develop calibration relationships between the bed shear stress (which is difficult to measure directly in routine deployments) and the flume centerline flow velocity, which is routinely measured. An example of a successful deployment of the flume is presented. The limitations and potential for further improvements are also briefly discussed.