Application of Hausdorff fractal derivative to the determination of the vertical sediment concentration distribution

The Rouse formula and its variants have been widely used to calculate the steady-state vertical concentration distribution for suspended sediment in steady sediment-laden flows, where the diffusive flux is assumed to be Fickian. Turbulent flow, however, exhibits fractal properties, leading to non-Fickian diffusive flux for sediment particles. To characterize non-Fickian dynamics of suspended sediment, the current study proposes a Hausdorff fractal derivative based advection-dispersion equation(H...     

Monitoring alluvial sand suspension by eddy correlation

Eddy correlation techniques are standard tools in micrometeorology and oceanography to measure momentum and contaminant transport across turbulent boundary layers. They can, in theory, be used to estimate the net vertical suspended sediment flux directly over different areas of an alluvial channel boundary, and thus disclose ongoing erosion/deposition patterns. The basic principles and main problems in applying the technique to alluvial suspension are first introduced. Results from a trial application of the method in a large sand bed river are then presented; the focus of the analysis is on the substantial (and surprising) contributions of multi-minute flow fluctuations to suspension work in the study environment. The data were collected in a 10 m deep channel of the Fraser River near Mission, British Columbia, Canada. Turbulent fluctuations of flow components streamwise and normal to the bed, along with the output of an optical suspended sediment sensor, were monitored over 7 h, 1 m above the bed. Flow velocities averaged 0·9 ms^?1 and mean suspended sediment concentrations 500 mgl^?1, at sensor level above 1–5 dm high dunes. Spectral analysis of the records reveals that approximately 30 per cent of the vertical suspended sand mixing across the sensor level (and roughly as much of the momentum exchange) was linked to gradual flow oscillations with periods between 1 and 13·6 min (underlying briefer, turbulent fluctuations). Extended periods of sediment-rich, slightly upward directed but slower mean flow alternated with periods of sediment-poor, slightly downward and faster mean flow; these slow fluctuations involved 10–20 cms^?1 changes in 5 min average flow speed, 2–4· changes in vertical flow angle and 100 mgl^?1 changes in mean sand concentration. To obtain accurate eddy-correlation estimates of the vertical suspension flux in the study conditions, hour-scale flow and turbidity records that include many of these multi-minute cycles appear to be necessary. The spectra of the Fraser River near-bed signals do not conspicuously differ in overall shape (in terms of low-frequency content and location of peak) from turbulent spectra encountered in some atmospheric boundary layers. Nonetheless, the long period fluctuations observed on the Fraser River may not be turbulent; rather they may reflect slowly evolving perturbations in the near-bed streamlines, caused by bedform translation or gradual fluctuation within the large-scale streamwise cells of the secondary flow.     

Tide-induced vertical suspended sediment concentration profiles: phase lag and amplitude attenuation

In tidal environments, the response of suspended sediment concentration (SSC) to the current velocity is not instantaneous, the SSC lagging behind the velocity (phase lag), and the amplitude of SSC variation decreasing with height above the bed (amplitude attenuation). In order to quantitatively describe this phenomenon, a one-dimensional vertical advection–diffusion equation of SSC is derived analytically for uniform unsteady tidal flow by defining a concentration boundary condition using a constant vertical eddy diffusivity and sediment settling velocity. The solution, in simple and straightforward terms, shows that the vertical phase lag increases linearly with the height above the bed, while the amplitude of the SSC variation decreases exponentially with the height. The relationship between the SSC and the normalized current velocity can be represented by an ellipse or a line, depending on the phase lag. The lag of sediment movement or “diffusion/settling lag” is the mechanism generating the phase lag effect. Field observations used for validation show that the theoretically predicted and the observed curves of the vertical SSC phase lag and amplitude attenuation show reasonable agreement. The procedure proposed in this paper substantially simplifies the modeling of suspended matter transport in tidal flows.     

Turbulent kinetic energy and sediment resuspension due to wave groups

Wave-induced sediment resuspension in nearshore regions has been observed occurring in an event-like manner and associated with the passage of wave groups. This paper describes field measurements of turbulent velocities obtained simultaneously with suspended sediment concentration and water surface elevation from Floreat Beach, Perth, Western Australia. The data were used to study the relationship between turbulent kinetic energy (TKE) on suspension events caused by wave groups and the intermittent nature of bottom turbulence production and sediment suspension. The field measurements showed the high TKE events occurred under wave crests, and sometimes under wave toughs, when the wave heights were increasing during the passage of a wave group; the TKE decreased after the maximum wave in the wave group had passed over the measurement location. High suspended sediment concentrations (ssc) and the intermittent high TKE events were not related rather the higher ssc events were associated with a secondary peak in the surface elevation, close to the maxima in the offshore velocity, and “burst” events in the Reynolds stress.     

The influence of asymmetries in overlying stratification on near-bed turbulence and sediment suspension in a partially mixed estuary

Data collected from the York River estuary demonstrate the importance of asymmetries in stratification to the suspension and transport of fine sediment. Observations collected during two 24-h deployments reveal greater concentrations of total suspended solids during the flood phase of the tide despite nearly symmetric near-bed tidal current magnitude. In both cases, tidally averaged net up-estuary sediment transport near the bed was clearly observed despite the fact that tidally averaged residual near-bed currents were near zero. Tidal straining of the along-channel salinity gradient resulted in a stronger pycnocline lower in the water column during the ebb phase of the tide and appeared to limit sediment suspension. Indirect measurements suggest that the lower, more intense, pycnocline on the ebb acted as a barrier, limiting turbulent length scales and reducing eddy diffusivity well below the pycnocline, even though the lower water column was locally well mixed. In order to more conclusively link changes in stratification to properties of near-bed eddy viscosity and diffusivity, longer duration tripod and mooring data from an additional experiment are examined, that included direct measurement of turbulent velocities. These additional data demonstrate how slight increases in stratification can limit vertical mixing near the bed and impact the structure of the eddy viscosity below the pycnocline. We present evidence that the overlying pycnocline can remotely constrain the vertical turbulent length scale of the underlying flow, limiting sediment resuspension. As a result, the relatively small changes in stratification caused by tidal straining of the pycnocline allow sediment to be resuspended higher in the water column during the flood phase of the tide, resulting in preferential up-estuary transport of sediment.Responsible Editor: Iris Grabemann     

Spreading of Stratified Currents in Lowland Reservoirs

The results of comprehensive hydrophysical studies of gradient and density-induced gravitational currents with thermal stratification in valley reservoirs are considered. The lengthwise and vertical development of currents as well as their evolution is considered. Local swells are detected in the near-bed nepheloid layer and clouds of suspended materials are found to be ejected from the density-induced current near abrupt changes in the bed relief. The near-bed density-induced current is found to strongly interact with the drift current in the presence of inner wave and variable-direction wind. The measured vertical profiles of velocity in the sections along the axis of the current and the longitudinal distributions of the average flow velocity and suspended material concentration are found to agree with model calculations.     

Suspended sediment concentration and the ripple–dune transition

Flume experiments were conducted in order to monitor changes in flow turbulence intensity and suspended sediment concentration at seven stages across the ripple–dune transition and at three different positions above the bed surface. Three‐dimensional velocity measurements were obtained using an acoustic Doppler velocimeter (ADV). Suspended sediment concentration (SSC) was monitored indirectly using ADV signal amplitude. Although limited to time‐averaged parameters, the analysis reveals that SSC varies significantly with stage across the transition and with sampling height. The statistical analysis also reveals an apparent uniformity of suspended sediment concentration with height above the bed in the lower half of the flow depth at the critical stage in the transition from ripples to dunes. This is also the stage at which turbulence intensity is maximized. Statistically significant correlations were also observed between suspended sediment concentrations and root‐mean‐square values of vertical velocity fluctuations. These correlations reflect the various levels of shear‐layer activity and the distinct turbulent flow regions across the transition. Conversely, time‐averaged values of Reynolds shear stress exhibit a very weak relationship with suspended sediment concentrations. Copyright © 2004 John Wiley & Sons, Ltd.     

An explanation for salinity- and SPM-induced vertical countergradient buoyancy fluxes

Measurements of turbulent fluctuations of velocity, salinity, and suspended particulate matter (SPM) are presented. The data show persistent countergradient buoyancy fluxes. These countergradient fluxes are controlled by the ratio of vertical turbulent kinetic energy (VKE) and available potential energy (APE) terms in the buoyancy flux equation. The onset of countergradient fluxes is found to approximately coincide with larger APE than VKE. It is shown here that the ratio of VKE to APE can be written as the square of a vertical Froude number. This number signifies the onset of the dynamical significance of buoyancy in the transport of mass. That is when motions driven by buoyancy begin to actively determine the vertical turbulent transport of mass. Spectral and quadrant analyses show that the occurrence of countergradient fluxes coincides with a change in the relative importance of turbulent energetic structures and buoyancy-driven motions in the transport of mass. Furthermore, these analyses show that with increasing salinity-induced Richardson number (Ri), countergradient contributions expand to the larger scales of motions and the relative importance of outward and inward interactions increases. At the smaller scales, at moderate Ri, the countergradient buoyancy fluxes are physically associated with an asymmetry in transport of fluid parcels by energetic turbulent motions. At the large scales, at large Ri, the countergradient buoyancy fluxes are physically associated with convective motions induced by buoyancy of incompletely dispersed fluid parcels which have been transported by energetic motions in the past. Moreover, these convective motions induce restratification and enhanced settling of SPM. The latter is generally the result of salinity-induced convective motions, but SPM-induced buoyancy is also found to play a role.     

Fine sediment carrying capacity of combined wave and current flows

The so-called fine sediment in many coastal areas and estuaries in China is mostly referred to the mixture of cohesive sediment and non-cohesive sediment. To predict the mixed type time sediment transport, sediment carrying capacity formulae combined with the 2-D suspended sediment transport equation and morphologic equation have been widely used in China. In the present study, the sediment carrying capacity formula suggested by Dou et al. （1995） for wave conditions has been improved and implemented for the prediction of sediment transport in nearshore regions where wave activities are significant. The improvement is based on the wave energy dissipation principle inside and outside the surf zone. In the improved formula, sediment in suspension increases with the magnitude of the wave period and this feature complies with general observations. More than 300 laboratory and field measured data sets have been reviewed and 12 of them have been used to verify and determine the major coefficients in the improved formula. The application of the sediment carrying capacity model in combined wave and current situations shows that the model can faithfully reproduce the cross-shore sediment concentration distributions at the southwest coast of Bohai Bay.     

Monitoring the physical forcing of resuspension events in the Thermaikos Gulf—NW Aegean during 2001–2003

This work constitutes an attempt to assess the relative importance of natural versus anthropogenic forcing for sediment resuspension on the shelf of the Thermaikos Gulf (NW Aegean) through a 2-year experiment in the framework of the E.U. project INTERPOL. Four periods of different hydrographic characteristics were identified, including two periods of stronger vertical homogenisation and two of stratified conditions. The former periods were characterized by stronger near-bed currents, while relatively weak internal wave motions dominated the periods of stratification. The near-bed currents showed strong coherence with the wind during the period of full homogenisation, whereas during stratification periods the wind provided indirect forcing evident mostly in the internal-wave bands. The site was too deep for the surface waves to cause any sediment resuspension. In conclusion, the observed near-bed currents at the site of interest did not appear to produce significant local resuspension of sediment; notably, the current-turbidity correlation suggested a shoreward transport of suspended material. The large-scale turbidity variability was rather related to the onset of the trawling period in mid-October 2001 and the increased riverine discharge in late summer/autumn 2002.     

Fine sediment dynamics in a shallow lake and implication for design of hydraulic works

Lake Markermeer is a large (680?km²), shallow body of water in the middle of the Netherlands, with a mean water depth of 3.6?m. One of the major problems in the lake is its decreasing ecological value which is, among other reasons, caused by a gradual increase of suspended sediment concentration and associated increase of light attenuation in the water column. A thorough understanding of fine sediment dynamics in the lake is a prerequisite for solving this problem. This paper addresses the 3D nature of near-bed sediment dynamics in Lake Markermeer, based on data sampled from a 1-month field experiment in autumn 2007. The campaign involved the collection of 71 bed samples across the lake. At each location, dual-frequency echo soundings were carried out to assess the thickness of the silt layer, and sediment concentration throughout the water column was measured with an Optical Backscatter Sensor (OBS). Moreover, 2-week time series of wave height, water level, current velocities, and near-bed sediment concentration were collected at a single location. The time series of sediment concentration were measured with a regular OBS and an Argus Surface Meter IV (ASM). During the measurement period, flow velocities ranged between 2 and 15?cm/s, wave heights up to 1.2?m were observed and turbidity levels varied between 40?mg/l to more than 300?mg/l. The ASM data generally showed uniform concentration profiles. However, profiles with steep concentration gradients near the bed were found for wave heights above 0.5?m. The field experiments further revealed pronounced 3D structures near the bed during discrete storms. The results are generalized for a wider range of conditions and across the full water depth through application of a 1DV point model, using a two-fraction representation of the grain size distribution. The fine and coarse fractions are found to resuspend rapidly for wind speeds above 5?m/s and 10??2?m/s, respectively, forming a uniform concentration profile if these wind conditions persists. High-concentration (???g/l) layers near the bed, containing the coarse sediment fraction, only occur at the onset and towards the end of a storm, when wind speed changes rapidly. It is under these conditions that horizontal gradients in layer density or thickness can transport considerable fine sediment. This transport provides an additional mechanism for the infill of, for instance, silt traps and navigation channels.     

On total turbulent energy and the passive and active role of buoyancy in turbulent momentum and mass transfer

Measurements of turbulent fluctuations of horizontal and vertical components of velocity, salinity and suspended particulate matter are presented. Turbulent Prandtl numbers are found to increase with stratification and to become larger than 1. Consequently, the vertical turbulent mass transport is suppressed by buoyancy forces, before the turbulent kinetic energy (TKE) and vertical turbulent momentum exchange are inhibited. With increasing stratification, the buoyancy fluxes do not cease, instead they become countergradient. We find that buoyantly driven motions play an active role in the transfer of mass. This is in agreement with trends derived from Monin–Obukhov scaling. For positive Richardson flux numbers (Ri _f ), the log velocity profile in the near-bed layer requires correction with a drag reduction. For negative Ri _f , the log velocity profile should be corrected with a drag increase, with increasing |Ri _f |. This highlights the active role played by buoyancy in momentum transfer and the production of TKE. However, the data do not appear to entirely follow Monin–Obukhov scaling. This is consistent with the notion that the turbulence field is not in equilibrium. The large stratification results in the decay of turbulence and countergradient buoyancy fluxes act to restore equilibrium in the energy budget. This implies that there is a finite adjustment timescale of the turbulence field to changes in velocity shear and density stratification. The energy transfers associated with the source and sink function of the buoyancy flux can be modeled with the concept of total turbulent energy.     

Burst-like sediment suspension events in a sand bed river

In a much quoted paper, Jackson (1976) hypothesized that turbulent [bursting] motions such as those documented in laboratory boundary layers play a major role in alluvial sediment suspension. To date, the hypothesis remained largely untested, due to difficulties in monitoring turbulent suspension in rivers. This study provides field data documenting burst-like turbulent motions over a sandy bed channel and quantifying the role of these motions in sand suspension. The data were collected in a 10 m deep channel of the Fraser River near Mission, British Columbia, Canada. Turbulent fluctuations of both flow components, downstream and normal to the bed, along with the output of an optical suspended sediment sensor, were monitored 1 m above the river bed. Typical flow velocities averaged 0·9 ms⁻¹ at the sensors, where mean suspended sediment concentrations were 500 mgl⁻¹; decimetre height small dunes on the backs of larger, half-metre amplitude dunes covered the channel bed in the area. Brief but intense, burst-like [ejection and inrush] events were identified in the flow records, where they are responsible for a high degree of [intermittency] in shear stress over the dunes: 80 per cent of the turbulent momentum exchange across the 1 m level can be ascribed to such brief (3-8 s duration) events, active under 12 per cent of the time. In addition, the record of fluctuating sediment concentrations reveals these burst-like motions to be highly effective in vertically mixing suspended sediment and thus, ultimately, in maintaining suspended sediment transport above the dune bed. The bulk (60 and 90 per cent in two deployments) of the vertical sediment mixing was accomplished by intense events active some 10 per cent of the time. No discrete recurrence timescale for these ‘burst-like’ mixing events is evident, however. Rather, a continuous variation of return periods was observed as a function of the magnitude of vertical mixing event considered. To that extent, conceptual models of sediment transport in terms of burst events with a predictable recurrence such as proposed by Jackson (1976) may be misleading.     

CRITICAL CONDITION FOR THE INITIATION OF SUSPENSION

L INTRODUCTIONSediment particles move either as bed load or as suspended load, depending on thecharacteristics of flow condition and on the properties of the sediment particlethemselves. Exchange between bed load and bed material takes place directly, while thesuspended load, under general conditions, can hardly interact with the stationary bedwithout the bed load as a medium. It is necessary to take into full account theinteractions of suspended load, bed load and bed material when bed d…     

Mathematical modeling of the transportation competency of an ice-covered flow

A two-dimensional model was developed to study the effect of ice cover on the transportation competence of ice-covered flows. The model is based on the equations of motion, impurity transfer, turbulence energy, and the ratio of turbulent energy to turbulent kinetic energy with allowance made to the effect of turbulent energy bursts on solid surfaces bounding the flow. The turbulent bursts on solid boundaries of open and ice-covered flows are shown to have no effect on the structure of flows, characterized by their aver-aged characteristics, but considerably change the distribution of suspended sediment concentrations.     

Non-equilibrium concentration profile formulas of suspended sediment and their preliminary applications

The vertical concentration profiles in non-equilibrium sediment transport processes generally deviate from the equilibrium concentration distribution of suspended sediment. The non-equilibrium concentration profile formulas currently available are those of Han and Brown, respectively. However, the complexity of these formulas limits their use in practical calculations. To improve the usefulness of these formulas, the unknown parameters in Han’s formula are reduced from three to two, and the thre...     

Occurrence of bed load transport in the presence of stable clast

It is well-versed that transport occurrence is vital for in stream rehabilitation, river restoration and installment of sediment sampler on river beds. Current practice emulates the use of continuous pre-diction using reach-averaged approach. However, prediction of transport occurrence entails the use of binary model through the execution of logistic regression analysis. Bed load and turbulence data were physically measured at mountainous region with divergent surface bedform in its presence. The para-meterization and statistical approaches are treated in the similar fashion with multiple regression except for the test for model fit and model selection criterion. The parameters on near-bed turbulence char-acteristics at the entrainment threshold were assigned as independent variables containing 15 pre-dictors. Almost 80 models were generated by selecting the best possible combination in accordance with the statistical precaution of alleviating multicollinearity issue. It is postulated that the model containing shields stress in the form of turbulent kinetic energy (TKE) at vertical direction and fractional time for second quadrant provides better estimation of potential location for greatest sediment-entrainment;hence a high possibility for transport occurrence.     

Parameterization of near-bed processes under collinear wave and current flows from a two-phase sheet flow model

Sediment transport models require appropriate representation of near-bed processes. We aim here to explore the parameterizations of bed shear stress, bed load transport rate and near-bed sediment erosion rate under the sheet flow regime. To that end, we employ a one-dimensional two-phase sheet flow model which is able to resolve the intrawave boundary layer and sediment dynamics at a length scale on the order of the sediment grain. We have conducted 79 numerical simulations to cover a range of collinear wave and current conditions and sediment diameters in the range 210–460 μm$\mathrm{\mu }\mathrm{m}$. The numerical results confirm that the intrawave bed shear stress leads the free stream velocity, and we assess an explicit expression relating the phase lead to the maximum velocity, wave period and bed roughness. The numerical sheet flow model is also used to provide estimates for the bed load transport rate and to inspect the near-bed sediment erosion. A common bed load transport rate formulation and two typical reference concentration approaches are assessed. A dependence of the bed load transport rate on the sediment grain diameter is observed and parameterized. Finally, the intrawave near-bed vertical sediment flux is further investigated and related to the time derivative of the bed shear stress.     

Concentration profiles for fine and coarse sediments suspended by waves over ripples: An analytical study with the 1-DV gradient diffusion model

Field and laboratory measurements of suspended sediments over wave ripples show, for time-averaged concentration profiles in semi-log plots, a contrast between upward convex profiles for fine sand and upward concave profiles for coarse sand. Careful examination of experimental data for coarse sand shows a near-bed upward convex profile beneath the main upward concave profile. Available models fail to predict these two profiles for coarse sediments. The 1-DV gradient diffusion model predicts the main upward concave profile for coarse sediments thanks to a suitable β(y)$\beta (y)$-function (where β$\beta$ is the inverse of the turbulent Schmidt number and y   is the distance from the bed). In order to predict the near-bed upward convex profile, an additional parameter α$\alpha$ is needed. This parameter could be related to settling velocity (α$\alpha$ equal to inverse of dimensionless settling velocity) or to convective sediment entrainment process. The profiles are interpreted by a relation between second derivative of the logarithm of concentration and derivative of the product between sediment diffusivity and α$\alpha$.     

Investigation into the application of cross-correlation analysis on acoustic backscattered signals from suspended sediments to measure nearbed current profiles

In the present work, the potential of correlation methods applied to acoustic signals backscattered from suspended sediments, is examined with regard to the measurement of near-bed vertical profiles of the horizontal current velocity. The technique uses the cross-correlation of the backscattered signal between pairs of downward looking horizontally separated transducers, to measure the time taken for suspension structures to advect from one transducer to another. This approach requires a degree of spatial coherence in the suspension field, and advantage is taken of this coherence to measure the flow. To investigate the technique, backscattered data collected using an array of transducers has been examined. The array was deployed along stream in an estuarine environment, which was subject to strong rectilinear currents, and high levels of suspended sediment concentration. Using pairs of transducers with separations between 0.25–5.42 m, the structure of the suspension field has been assessed, the implication of these observations for measuring flow discussed, and nearbed measurements of current profiles obtained. The results show that in the estuarine environment investigated, if the transducer pair separation was of the order of a metre or less, and currents were sufficient to retain sediments in suspension, vertical profiles of the horizontal current could be measured. To assess the results conventional electromagnetic and impeller current meter measurements were collected at four heights above the bed. Comparison of the conventional reference measurements with the cross-correlation velocities show that the correlation method has the potential to provide reliable measurements of near-bed current profiles.