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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.

The paper briefly outlines the double-averaging methodology for studying environmental rough-bed flows. It focuses on the applications of this methodology in environmental hydraulics by providing several examples illustrating advantages of this methodology over conventional approaches. Examples include: (1) identification of specific flow layers and flow types; (2) vertical distribution of the double-averaged velocity between the roughness tops and troughs; (3) vertical distribution of momentum fluxes and sinks for typical roughness types due to turbulence, mean flow heterogeneity, secondary currents, form drag, and viscous drag; (4) estimates of form-induced (dispersive) stresses and evaluation of their structure using quadrant analysis; and (5) closure development for mass-transfer-uptake processes for stream periphyton. These examples illustrate the advantages of the double-averaging methodology over conventional approaches as well as highlight its potential for studying flows over very rough beds, hig...

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.

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 roughness, 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 CD =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 tops can be calculated using either the double average of the square ...

A series of experiments was undertaken to assess fully rough turbulent subcritical flow over two-dimensional transverse repeated-rib roughness of varying spacing λ∕h=1–16 (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 (λ∕h

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.

Propagule dispersal in seaweeds is a process influenced by a variety of biological and physical factors, the complexity of which has hindered efforts to understand colonization, persistence, post-disturbance recovery, and dynamics of algal populations in general. In view of this limitation, we employ here modifications to an existing turbulent-transport model to explore the mechanics of nearshore macroalgal spore dispersal and its relationship to coastal hydrodynamic conditions. Our modeling efforts focus on four example species of seaweed whose reproductive propagules span a wide range in sinking speed and height of release above the sea floor: the giant kelp Macrocystis pyrifera, the erect fucoid Sargassum muticum, the small filamentous brown alga Ectocarpus siliculosus, and the flaccid red alga Sarcodiotheca gaudichaudii. Results indicate that both propagule sinking speed and release height can affect dispersal distance substantially, but that the influence of these biological parameters is modulated strongly by the intensity of turbulence as dictated by waves and currents. In rapid flows with larger waves, it is primarily fluid dynamic processes, in particular current velocities, that determine dispersal distance. Additional simulations suggest that patterns of spore dispersal are highly skewed, with most propagules encountering the sea floor within a few meters to hundreds of meters of their parents, but with a sizeable fraction of spores also dispersing as far as kilometers. Such model predictions imply a much greater potential for longer range dispersal than has typically been assumed, a finding with important implications for understanding the demographics of algal populations and for predicting levels of connectivity among them.

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.

To estimate bed-load sediment transport rates in flows over bed forms such as ripples and dunes, spatially averaged velocity profiles are frequently used to predict mean boundary shear stress. However, such averaging obscures the complex, nonlinear interaction of wake decay, boundary-layer development, and topographically induced acceleration downstream of flow separation and often leads to inaccurate estimates of boundary stress, particularly skin friction, which is critically important in predicting skin friction over 2D bed forms. The approach is based on combining the equations describing the mechanics of the internal boundary layer with semi-empirical structure functions to predict the velocity at the crest of a bed form, where the flow is most similar to a uniform boundary layer. Significantly, the methodology is directed toward making specific predictions only at the bed-form crest, and as a result it avoids the difficulty and questionable validity of spatial averaging. The model provides an accurate estimate of the skin friction at the crest where transport rates are highest. Simple geometric constraints can be used to derive the mean transport rates as long as bedload is dominant.

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.

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.

The net transport of sediment by suspension is calculated by integrating the product of the sediment concentration and velocity over the water depth. For many flows, accurate calculations must incl...

The stability of ripples and dunes in flows of finite depth are investigated for the linear, small-amplitude case and also for the more realistic finite-amplitude situation. For the former perturbation approach is taken, leading to the general result that, without the inclusion of some lag between the sediment transport rate and the boundary shear stress, all wavelengths are unstable. This results from an upstream shift in the stress relative to the bedform, leading to deposition at the crest. By assuming a realistic lag based on the mechanics of bed load transport, a fastest growing wave at ripple-scales results: similarly, if suspended sediment were included, longer lags result and a dune-scale instability could result. Some investigators have invoked a gravitational effect, arguing that sediment transport is enhanced downslope and retarded upslope. This creates an effective downstream shift in the transport rate and some argue that both ripple and dune instabilities result, however, a realistic evaluation of this effect shows that it is much too small to be effective. Naturally occurring bedforms are of finite-amplitude; typically they are asymmetrical, often causing flow separation. This highly non-linear process creates a vastly different flow environment from that assumed in the initial stability case. A wake-like flow structure develops downstream of the separation zone and an internal boundary layer develops beneath. The complex interaction of these two different flow regimes as well as the effect induced by the topography of the bedform itself, produces a shear stress field that dictates the stability of the feature itself.

[1] 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.

[1] 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.

[1] A series of detailed measurements were made of unidirectional turbulent open-channel flow over fixed, artificial, sinuous-crested three-dimensional (3-D) dune shapes. The response of the mean free surface was two-dimensional (2-D). Mean streamwise velocities were largest over the node of the sinuous dune crest line rather than over the maxima or minima of the crest line. Friction coefficients of the 3-D dunes were 50% higher on average in comparison to those of their 2-D counterparts when subjected to flows of similar depths and discharges. Despite the larger friction of the 3-D dunes, the turbulence generated by them was much weaker than that generated by their 2-D counterparts. The spatial structure of turbulence caused by the sinuous crest line of the 3-D dunes was correlated with the presence of secondary currents. These secondary current cells directed flow upward in the regions where the streamwise velocities were low and downward in the regions where streamwise velocities were high, suggesting that they could be responsible for a significant amount of momentum flux not being carried by the low turbulent stresses over the 3-D dunes.

We report the case of a 38-year-old male with metastatic ductal eccrine adenocarcinoma (DEA) of the left breast responding to 5-fluorouracil, epirubicin, and cyclophosphamide (FEC) chemotherapy. This patient presented with a 2-week history of difficulty walking due to bilateral hip and lower back pain. Examination revealed an ulcerating cutaneous mass over the left anterior chest wall, left axillary lymphadenopathy, and tenderness over the spine. Investigations, including a punch biopsy of the breast lesion, a CT scan of the thorax,a sonogram of the liver, and a bone scan, were performed, and the patient was originally diagnosed as having metastatic invasive ductal carcinoma (IDC). Radiotherapy was administered to the bony metastases, and he was started on six cycles of FEC chemotherapy. Referral was made to our institution, where the original punch biopsy was reviewed. The tumor cells were polygonal with darkly stained pleomorphic nuclei and abundant eosinophilic cytoplasm and were localized to areas of fibrotic stroma containing eccrine glands and ducts and did not appear to involve mammary tissue. Cells with foamy cytoplasm were observed, a characteristic suggestive of sebaceous gland differentiation. Immunohistochemical studies revealed that the tumor cells were CK7 and GCDFP-15/PIP negative and ERα positive. Both the morphologic and immunohistochemical characteristics of the tumor were consistent with a revised diagnosis of DEA rather than IDC. Symptomatic and radiologic responses to the FEC chemotherapy were subsequently noted. Tamoxifen and ibandronate were given postchemotherapy, and the patient remains pain free 1 year after his original presentation. This case highlights the challenge in discriminating histopathologically between two rare tumors of the male breast, namely DEA and IDC. In addition, clinical response to FEC by metastatic DEA has not been previously documented, and this therapeutic regimen warrants further consideration for the treatment of locally advanced or metastatic DEC.

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 roughne...

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

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.

Calculation of suspended sediment transport rates requires integration of the product of sediment concentration times velocity over the depth of the flow; hence accurate profiles of these quantities are required especially near the sediment bed. Although this would appear to be a straightforward task, many effects can cause significant deviation of these quantities from those values expected from simple known relationships. For example, density stratification by suspended particulates can dampen turbulence fluctuations and significantly reduce the effective viscosity and diffusivity of the flow. The momentum and suspended sediment equations are solved herein, including the effects of stratification by suspended sediment and the effects due to size distribution and bedforms. The results show that stratification and bedforms generally reduce the transport capacity of the flow, whereas treating the sediment as an assemblage of different sizes rather than a single size (D50) increases the expected transport.

In order to predict the response of deep ocean sediments to the near-bottom currents, accurate estimates of the near-bottom velocity and the boundary shear stress are necessary. Because of the unsteady nature of deep ocean currents, dynamic models are required. This can be accomplished either by time stepping methods or by the use of Fourier transform techniques. Here the latter is applied to the momentum equation and the results are compared to data from the HEBBLE region in the North Atlantic Ocean. An eddy viscosity is employed for closure; however, because the unsteady nature of the problem requires it to vary in time, the uniform one-dimensional Ekman layer equations become nonlinear. Results show that if the Fourier transform method includes the turbulence adjustments in this way, it predicts very accurately both stress and velocity fields.

Sand ribbons typically are shallow-water sedimentary features characterized as thin, elongate bands of sand overlying a coarser lag sediment which is exposed between them. The ribbons are oriented along the direction of the dominant current, and are formed by a secondary circulation pattern that includes a small component of the boundary shear stress directed toward the center of the sand ribbons. A perturbation expansion, coupled with flume experiments, indicates that this circulation pattern is linked to differences in the bottom roughness between the sand ribbons and the adjacent coarser strips. The non-uniform turbulence field arising from this roughness distribution drives a secondary helical flow. The expansion indicates that there is a preferred ratio of sand ribbon spacing to water depth (∼4:1) for unstratified channel flow conditions. The secondary flow pattern forces the downstream flow to readjust so that the boundary shear stress over the smooth sand strips is considerably smaller than the mean stress. This serves to retard the movement of sand through such a system.

Under the influence of short ultraviolet radiation, diphenylamine and nitrate salts react to produce a yellow-colored product. The reaction appears specific and makes it possible to detect 1 μg. of nitrate ion in 0.01 ml. of solution.

Under the activating influence of short-wave ultraviolet light, diphenylamine and nitrate ions in solution or on filter paper react to yield a yellow-colored product. Between pH 4 and 10 this consists mainly of 2-nitrodiphenylamine and 4-nitrodiphenylamine. Over this range of pH, the absorption maxima at 405 mμ did not shift; however, the intensity of absorption appeared to reach a minimum at or near neutrality and then increase rapidly as the solution was made more alkaline. The reaction rate was not affected by lowering the concentration of diphenylamine from 0.38% to 0.038%. A similar change in nitrate concentration decreased the rate 5.4 times. No evidence of nitroso compounds was found. Possible mechanisms are suggested.

A knowledge of the transport of sediment in a shallow, high energy environment such as the North Sea is important to the general understanding of such a system. The shape of the basin itself is largely a product of the interaction between the currents and the sediments. The engineers are interested in maintaining harbors and predicting morphological adjustments caused by man-made alterations of currents. The environmentally conscious are concerned about pollution and water quality which both are often strongly linked to the sediments. Sediment transport involves a complex interaction between the flow and the bottom. Ultimately an accurate knowledge of the forces acting on the bottom (i.e., the boundary shear stress) is necessary in order to predict the initiation of sediment movement and subsequent transport rates. In the North Sea this is complicated by the unsteady nature of the flow. This arises from both storms and tides. In order to better understand such a system, it was decided to begin by investigating the boundary layer in regions of active transport where the flow was dominated by tidal effects.