Characterization of bedload intermittency near the threshold of motion using a Lagrangian sediment transport model

At the smallest scales of sediment transport in rivers, the coherent structures of the turbulent boundary layer constitute the fundamental mechanisms of bedload transport, locally increasing the instantaneous hydrodynamic forces acting on sediment particles, and mobilizing them downstream. Near the critical threshold for initiating sediment motion, the interactions of the particles with these unsteady coherent structures and with other sediment grains, produce localized transport events with brief episodes of collective motion occurring due to the near-bed velocity fluctuations. Simulations of these flows pose a significant challenge for numerical models aimed at capturing the physical processes and complex non-linear interactions that generate highly intermittent and self-similar bedload transport fluxes. In this investigation we carry out direct numerical simulations of the flow in a rectangular flat-bed channel, at a Reynolds number equal to Re = 3632, coupled with the discrete element method to simulate the dynamics of spherical particles near the bed. We perform two-way coupled Lagrangian simulations of 48,510 sediment particles, with 4851 fixed particles to account for bed roughness. Our simulations consider a total of eight different values of the non-dimensional Shields parameter to study the evolution of transport statistics. From the trajectory and velocity of each sediment particle, we compute the changes in the probability distribution functions of velocities, bed activity, and jump lengths as the Shields number increases. For the lower shear stresses, the intermittency of the global bedload transport flux is described by computing the singularity or multifr actal spectrum of transport, which also characterizes the widespread range of transport event magnitudes. These findings can help to identify the mechanisms of sediment transport at the particle scale. The statistical analysis can also be used as an ingredient to develop larger, upscaled models for predicting mean transport rates, considering the variability of entrainment and deposition that characterizes the transport near the threshold of motion.     

Large eddy simulation of flow and scalar transport in a vegetated channel

Predicting flow and mass transport in vegetated regions has a broad range of applications in ecology and engineering practice. This paper presents large eddy simulation (LES) of turbulent flow and scalar transport within a fully developed open-channel with submerged vegetation. To properly represent the scalar transport, an additional diffusivity was introduced within the canopy to account for the contribution of stem wakes, which were not resolved by the LES, to turbulent diffusion. The LES produced good agreement with the velocity and concentration fields measured in a flume experiment. The simulation revealed a secondary flow distributed symmetrically about the channel centerline, which differed significantly from the circulation in a bare channel. The secondary circulation accelerated the vertical spread of the plume both within and above the canopy layer. Quadrant analysis was used to identify the form and shape of canopy-scale turbulent structures within and above the vegetation canopy. Within the canopy, sweep events contributed more to momentum transfer than ejection events, whereas the opposite occurred above the canopy. The coherent structures were similar to those observed in terrestrial canopies, but smaller in scale due to the constraint of the water surface.     

Turbulence investigation in the roughness sub-layer of a near wall flow

The turbulence behaviour along a wall roughened by pyramidal elements was analysed in the region extending from the apex of the roughness elements up to the external limit of the roughness sub-layer. The data used for the analysis were obtained by particle image velocimetry technique. The rough wall turbulent boundary layer flow is characterized by a relatively low Reynolds number. All the results on the rough wall were compared with data referring to the canonical flow on a smooth wall turbulent boundary layer. Mean values and turbulence quantities for the two flows collapse when approaching the external limit of the roughness sublayer. The quadrant analysis of the Reynolds shear stress, in the region near the surface, shows that the contribution of the sweep motions is about equivalent for the two flows (except for wall distances lower than 40 viscous units). The contribution of the ejection motions appears to be more important over the smooth wall than over the rough wall with increasing differences approaching the wall. The probability density functions of the streamwise fluctuating velocity field for the rough wall case appear to be positively skewed in the zone very close to the pyramid apex, in contrast with the behavior observed for the smooth wall case at corresponding distances from the wall. The integral and Taylor scales for the rough wall case appear to be strongly reduced by the presence of the roughness, while the Kolmogorov microscale shows higher values.     

Interaction between flow, transport and vegetation spatial structure

This paper summarizes recent advances in vegetation hydrodynamics and uses the new concepts to explore not only how vegetation impacts flow and transport, but also how flow feedbacks can influence vegetation spatial structure. Sparse and dense submerged canopies are defined based on the relative contribution of turbulent stress and canopy drag to the momentum balance. In sparse canopies turbulent stress remains elevated within the canopy and suspended sediment concentration is comparable to that in unvegetated regions. In dense canopies turbulent stress is reduced by canopy drag and suspended sediment concentration is also reduced. Further, for dense canopies, the length-scale of turbulence penetration into the canopy, δ _e , is shown to predict both the roughness height and the displacement height of the overflow profile. In a second case study, the relation between flow speed and spatial structure of a seagrass meadow gives insight into the stability of different spatial structures, defined by the area fraction covered by vegetation. In the last case study, a momentum balance suggests that in natural channels the total resistance is set predominantly by the area fraction occupied by vegetation, called the blockage factor, with little direct dependence on the specific canopy morphology.     

Mixing at a sediment concentration interface in turbulent open channel flow

In this work we address the role of turbulence on mixing of clear layer of fluid with sediment-laden layer of fluid at a sediment concentration interface. This process can be conceived as the entrainment of sediment-free fluid into the sediment-laden layer, or alternatively, as the transport of sediment into the top sediment-free flow. This process is governed by four parameters—Reynolds number of the flow \(Re_\tau\), non-dimensional settling velocity of the sediment (proxy for sediment size) \(\tilde{V}\), Richardson number \(Ri_\tau\) and Schmidt number Sc. For this work we have performed direct numerical simulations for fixed Reynolds and Schmidt numbers while varying the values of Richardson number and particle settling velocity. In the simple model considered here, the flow’s momentum and turbulence pre-exists over the entire layer of fluid, while the sediment is initially confined to a layer close to the bed. Mixing of sediment-free fluid with the sediment-laden layer is associated primarily with upward transport of sediment and buoyancy. There is no simultaneous upward transport of fluid momentum and turbulence into the sediment-free fluid layer, which is already in motion and turbulent. The analysis performed shows that the ability of the flow to transport a given sediment size decreases with the distance from the bottom, and thus only fine enough sediment particles are transported across the sediment concentration interface. For these cases, the concentration profiles evolve to a final steady state in good agreement with the well-known Rouse profile. The approach towards the Rouse profile happens through a transient self-similar state. This behavior of the flow is not seen for larger particles. Detailed analysis of the three dimensional structure of the sediment concentration interface shows the mechanisms by which sediment particles are lifted up by tongues of sediment-laden fluid with positive correlation between vertical velocity and sediment concentration. Finally, the mixing ability of the flow is addressed by monitoring the time evolution of the center of mass of the sediment-laden layer and the vertical location of the sediment-free/sediment-laden interface.     

A mathematical model for type II profile of concentration distribution in turbulent flows

This paper presents a mathematical model to investigate type II profile of suspension concentration distribution (i.e., the concentration profile where the maximum concentration appears at some distance above the bed surface) in a steady, uniform turbulent flow through open-channels. Starting from the mass and momentum conservation equations of two-phase flow, a theoretical model has been derived. The distribution equation is derived considering the effects of fluid lift force, drag force, particle inertia, particle–particle interactions, particle velocity fluctuations and drift diffusion. The equation is solved numerically and is compared with available experimental data as well as with other models existing in the literature. Good agreement between the observed value and computed result, and minimum error in comparison to other models indicate that the present model can be applied in predicting particle concentration distribution for type II profile for a wide range of flow conditions. The proposed model is also able to show the transition from type I profile to type II profile.     

Mass Transport in Vegetated Shear Flows

Submerged aquatic vegetation has the potential to greatly improve water quality through the removal of nutrients, particulates and trace metals. The efficiency of this removal depends heavily upon the rate of vertical mixing, which dictates the timescale over which these constituents remain in the canopy. Continuous dye injection experiments were conducted in a flume with model vegetation to characterize vertical mass transport in vegetated shear flows. Through the absorbance–concentration relationship of the Beer–Lambert Law, digital imaging was used to provide high-resolution concentration profiles of the dye plumes. Vertical mass transport is dominated by the coherent vortices of the vegetated shear layers. This is highlighted by the strong periodicity of the transport and its simple characterization based on properties of the shear layer. For example, the vertical turbulent diffusivity is directly proportional to the shear and thickness of the layer. The turbulent diffusivity depends upon the size of the plume, such that the rate of plume growth is lower near the source. In the far-field, mass is mixed more than twice as rapidly as momentum. Finally, plume size is dictated predominantly by X, a dimensionless distance that scales upon the number of vortex rotations experienced by the plume.     

Near-boundary velocity and turbulence in depth-varying stream flows

This research examined the temporal distribution of turbulent structure near a streambank toe through the progression of a flood wave in West Run (Morgantown, WV, USA). Three-dimensional velocities and water depths were measured through a 17-h flood event. Turbulence characteristics were examined: Reynolds stresses, turbulent kinetic energy, and turbulence intensities. On average, near-boundary velocity during the rising stage was less than the falling stage, likely due to the measurement location and local roughness. The velocity vectors shifted from towards bed before the flood wave to toward the streambank during progression of the flood wave. Turbulent kinetic energy increased with increasing water depth during the rising stage. Reynolds stress, τ_xz, increased with increasing water depth during the rising stage, but the majority of the stresses were negative through the storm event. Reynolds stress, τ_xy, was positive throughout the event and did not vary with depth. This work is among the first to evaluate turbulence during depth-varying flows in the field.     

Mass conservation and atmospheric dynamics in the Regional Atmospheric Modeling System (RAMS)

This paper examines the spatio-temporal patterns of atmospheric carbon dioxide transport predicted by the Regional Atmospheric Modeling System (RAMS). Forty-eight hour simulations over northern New England incorporating a simple representation of the diurnal summertime surface carbon dioxide forcing arising from biological activity indicate that, in its native formulation, RAMS exhibits a significant degree of mass non-conservation. Domain-wide rates of non-physical mass gain and mass loss are as large as three percent per day which translates into approximately eleven parts per million per day for carbon dioxide — enough to rapidly dilute the signature of carbon dioxide fluxes arising from biological activity. Analysis shows that this is due to the approximation used by RAMS to compute the Exner function. Substitution of the exact, physically complete equation improves mass conservation by two orders of magnitude. In addition to greatly improving mass conservation, use of the complete Exner function equation has a substantial impact on the spatial pattern of carbon dioxide predicted by the model, yielding predictions differing from a conventional RAMS simulation by as much as forty parts per million. Such differences have important implications both for comparisons of modeled atmospheric carbon dioxide concentrations to observations and for carbon dioxide inversion studies, which use estimates of atmospheric transport of carbon dioxide in conjunction with measurements of atmospheric carbon dioxide concentrations to infer the spatio-temporal distribution of surface carbon dioxide fluxes. Furthermore, use of the complete Exner function equation affects the vertical velocity and water mixing ratio fields, causing significant changes in accumulated precipitation over the region.     

Coupling between free-surface fluctuations,velocity fluctuations and turbulent Reynolds stresses during the upstream propagation of positive surges,bores and compression waves

In open channel, canals and rivers, a rapid increase in flow depth will induce a positive surge, also called bore or compression wave. The positive surge is a translating hydraulic jump. Herein new experiments were conducted in a large-size rectangular channel to characterise the unsteady turbulent properties, including the coupling between free-surface and velocity fluctuations. Experiments were repeated 25 times and the data analyses yielded the instantaneous median and instantaneous fluctuations of free-surface elevation, velocities and turbulent Reynolds stresses. The passage of the surge front was associated with large free-surface fluctuations, comparable to those observed in stationary hydraulic jumps, coupled with large instantaneous velocity fluctuations. The bore propagation was associated with large turbulent Reynolds stresses and instantaneous shear stress fluctuations, during the passage of the surge. A broad range of shear stress levels was observed underneath the bore front, with the probability density of the tangential stresses distributed normally and the normal stresses distributed in a skewed single-mode fashion. Maxima in normal and tangential stresses were observed shortly after the passage of a breaking bore roller toe. The maximum Reynolds stresses occurred after the occurrence of the maximum free-surface fluctuations, and this time lag implied some interaction between the free-surface fluctuations and shear stress fluctuations beneath the surge front, and possibly some causal effect.     

Hierarchical modeling of the dilute transport of suspended sediment in open channels

We propose, discuss and validate a theoretical and numerical framework for sediment-laden, open-channel flows which is based on the two-fluid-model (TFM) equations of motion. The framework models involve mass and momentum equations for both phases (sediment and water) including the interactive forces of drag, lift, virtual mass and turbulent dispersion. The developed framework is composed by the complete two-fluid model (CTFM), a partial two-fluid model (PTFM), and a standard sediment-transport model (SSTM). Within the umbrella of the Reynolds-Averaged Navier-Stokes (RANS) equations, we apply K–ε type closures (standard and extended) to account for the turbulence in the carrier phase (water). We present the results of numerical computations undertaken by integrating the differential equations over control volumes. We address several issues of the theoretical models, especially those related to coupling between the two phases, interaction forces, turbulence closure and turbulent diffusivities. We compare simulation results with various recent experimental datasets for mean flow variables of the carrier as well as, for the first time, mean flow of the disperse phase and turbulence statistics. We show that most models analyzed in this paper predict the velocity of the carrier phase and that of the disperse phase within 10% of error. We also show that the PTFM provides better predictions of the distribution of sediment in the wall-normal direction as opposed to the standard Rousean profile, and that the CTFM is by no means superior to the PTFM for dilute mixtures. We additionally report and discuss the values of the Schmidt number found to improve the agreement between predictions of the distribution of suspended sediment and the experimental data.     

Froude scaling limitations in modeling of turbidity currents

The scaling problem associated with the modeling of turbidity currents has been recognized but is yet to be explored systematically. This paper presents an analysis of the dimensionless governing equations of turbidity currents to investigate the scale effect. Three types of flow conditions are considered: (i) conservative density current; (ii) purely depositional turbidity current; and (iii) mixed erosional/depositional turbidity current. Two controlling dimensionless numbers, the Froude number and the Reynolds number, appear in the non-dimensional governing equations. When densimetric Froude similarity is satisfied, the analysis shows that the results would be scale-invariant for conservative density current under the rough turbulent condition. In the case of purely depositional flows, truly scale-invariant results cannot be obtained, as the Reynolds-mediated scale effects appear in the bottom boundary conditions of the flow velocity and sediment fall velocity. However, the scale effect would be relatively modest. The Reynolds effect becomes more significant for erosional or mixed erosional/depositional turbidity currents as Reynolds-mediated scale effects also appear in the sediment entrainment relation. Numerical simulations have been conducted at three different scales by considering densimetric Froude scaling alone as well as combined densimetric Froude and Reynolds similarity. Simulation results confirm that although the scaling of densimetric Froude number alone can produce scale-invariable results for conservative density currents, variations occur in the case of turbidity currents. The results become scale invariant when densimetric Froude and Reynolds similarities are satisfied simultaneously.     

Monitoring the transport of biomass burning emissions in South America

The atmospheric transport of biomass burning emissions in the South American and African continents is being monitored annually using a numerical simulation of air mass motions; we use a tracer transport capability developed within RAMS (Regional Atmospheric Modeling System) coupled to an emission model. Mass conservation equations are solved for carbon monoxide (CO) and particulate material (PM2.5). Source emissions of trace gases and particles associated with biomass burning activities in tropical forest, savanna and pasture have been parameterized and introduced into the model. The sources are distributed spatially and temporally and assimilated daily using the biomass burning locations detected by remote sensing. Advection effects (at grid scale) and turbulent transport (at sub-grid scale) are provided by the RAMS parameterizations. A sub-grid transport parameterization associated with moist deep and shallow convection, not explicitly resolved by the model due to its low spatial resolution, has also been introduced. Sinks associated with the process of wet and dry removal of aerosol particles and chemical transformation of gases are parameterized and introduced in the mass conservation equation. An operational system has been implemented which produces daily 48-h numerical simulations (including 24-h forecasts) of CO and PM2.5, in addition to traditional meteorological fields. The good prediction skills of the model are demonstrated by comparisons with time series of PM2.5 measured at the surface.     

Hydrodynamics and contaminant transport on a degraded bed at a 90-degree channel confluence

Channel confluences at which two channels merge have an important effect on momentum exchange and contaminant diffusion in both natural rivers and artificial canals. In this study, a three-dimensional numerical model, which is based on the Reynolds Averaged Navier–Stokes equations and Reynolds Stress Turbulence model, is applied to simulate and compare flow patterns and contaminant transport processes for different bed morphologies. The results clearly show that the distribution of contaminant concentrations is mainly controlled by the shear layer and two counter-rotating helical cells, which in turn are affected by the discharge ratio and the bed morphology. As the discharge ratio increases, the shear flow moves to the outer bank and the counter-clockwise tributary helical cell caused by flow deflection is enlarged, leading the mixing happens near the outer bank and the mixing layer distorted. The bed morphology can induce shrinkage of the separation zone and increase of the clockwise main channel helical cell, which is initiated by the interaction between the tributary helical cell and the main channel flow and strengthened by the deep scour hole. The bed morphology can also affect the distortion direction of the mixing layer. Both a large discharge ratio and the bed morphology could lead to an increase in mixing intensity.     

Influence of the secondary motions on pollutant mixing in a meandering open channel flow

This paper presents large eddy simulation of turbulent flow in a meandering open channel with smooth wall and rectangular cross-section. The Reynolds number based on the channel height is 40,000 and the aspect ratio of the cross-section is 4.48. The depth-averaged mean stream-wise velocity agree well to experimental measurements. In this specific case, two interacting cells are formed that swap from one bend to the other. Transport and mixing of a pollutant is analysed using three different positions of release, e.g. on the inner bank, on the outer bank and on the centre of the cross section. The obtained depth-average mean concentration profiles are reasonably consistent with available experimental data. The role of the secondary motions in the mixing processes is the main focus of the discussion. It is found that the mixing when the scalar is released on the centre of the cross-section is stronger and faster than the mixing of the scalar released on the sides. When the position of release is close to a bank side, the mixing is weaker and a clear concentration of scalar close to the corresponding side-wall can be observed in both cases.     

The Reynolds transport theorem: Application to ecological compartment modeling and case study of ecosystem energetics

The Reynolds transport theorem (RTT) from mathematics and engineering has a rich history of success in mass transport dynamics and traditional thermodynamics. This paper introduces RTT as a complementary approach to traditional compartmental methods used in ecological modeling and network analysis. A universal system equation for a generic flow quantity is developed into a generic open-system differential expression for conservation of energy. Nonadiabatic systems are defined and incorporated into control volume (CV) and control surface (CS) perspectives of RTT where reductive assumptions in empirical data are then formally introduced, reviewed, and appropriately implemented. Compartment models are abstract, time-dependent systems of simultaneous differential equations describing storage and flow of conservative quantities between interconnected entities (the compartments). As such, they represent a set of flexible and somewhat informal, assumptions, definitions, algebraic manipulations, and graphical depictions subject to influence and selectively parsed expression by the modeler. In comparison, RTT compartment models are more rigorous and formal integro-differential equations and graphics initiated by the RTT universal system equation, forcing an ordered identification of simplifying assumptions, ending with clearly identified depictions of the transfer and transport of conservative substances in physical space and time. They are less abstract in the rigor of their equation development leaving less ambiguity to modeler discretion. They achieve greater consistency with other RTT compartment style models while possibly generating greater conformity with physical reality. Characteristics of the RTT approach are compared with those of a traditional compartment model of energy flow in an intertidal oyster-reef community.     

Wind- and tide-induced currents in the Stagnone lagoon (Sicily)

The hydrodynamic circulation is analyzed in the coastal lagoon of Stagnone di Marsala, a natural reserve located in the north-western part of Sicily, using both experimental measurements and numerical simulations. Field measurements of velocities and water levels, carried out using an ultrasound sensor (3D), are used to validate the numerical model. A 3D finite-volume model is used to solve the Reynolds-averaged momentum and mass balance differential equations on a curvilinear structured grid, employing the k–e{\varepsilon} turbulence model for the Reynolds stresses. The numerical analysis allows to identify the relative contribution of the forces affecting the hydrodynamic circulation inside the lagoon. In the simulations only wind and tide forces are considered, neglecting the effects of water density changes. Two different conditions are considered. In the first both the wind stress over the free-surface and the tidal motion are imposed. In the second the wind action is neglected, to separately analyze the tide-induced circulation. The comparison between the two test cases highlights the fundamental role of the wind on the hydrodynamics of the Stagnone lagoon, producing a strong vertical recirculation pattern that is not observed when the flow is driven by tides only.     

Self-aeration in the rapidly- and gradually-varying flow regions of steep smooth and stepped spillways

In high-velocity chute flows, free-surface aeration is often observed. The phenomenon is called self-aeration or white waters. When the turbulent shear stresses next to the free-surface are large enough, air bubbles are entrained throughout the entire air–water column. A rapidly-varied flow region is observed immediately downstream of the inception point of free-surface aeration. An analytical solution of the air diffusion equation is proposed and the results compare well with new experimental data. Both experiments and theory indicate that the flow bulking spans over approximately 3–4 step cavities downstream of the inception point of free-surface aeration on a stepped chute. Further downstream the void fraction distributions follow closely earlier solutions of the air diffusion equation. The application of the diffusion equation solution to prototype and laboratory data shows air bubble diffusivities typically larger than the momentum transfer coefficient. The result highlights however a marked decrease in the ratio of air bubble diffusivity to eddy viscosity with increasing Reynolds number. The finding might indicate some limitation of laboratory investigations of air bubble diffusion process in self-aerated flows and of their extrapolation to full-scale prototype applications.     

Large-eddy simulation of starting buoyant jets

A series of Large Eddy Simulations (LES) are performed to investigate the penetration of starting buoyant jets. The LES code is first validated by comparing simulation results with existing experimental data for both steady and starting pure jets and lazy plumes. The centerline decay and the growth rate of the velocity and concentration fields for steady jets and plumes, as well as the simulated transient penetration rate of a starting pure jet and a starting lazy plume, are found to compare well with the experiments. After validation, the LES code is used to study the penetration of starting buoyant jets with three different Reynolds numbers from 2000 to 3000, and with a wide range of buoyancy fluxes from pure jets to lazy plumes. The penetration rate is found to increase with an increasing buoyancy flux. It is also observed that, in the initial Period of Flow Development, the two penetrative mechanisms driven by the initial buoyancy and momentum fluxes are uncoupled; therefore the total penetration rate can be resolved as the linear addition of these two effects. A fitting equation is proposed to predict the penetration rate by combining the two independent mechanisms.     

Similarity theory and parameterization of mixing in the upper ocean

Boundary layers with small thermal and mechanical inertia are close to steady-state conditions. This underlies the Monin-Obukhov similarity theory and explains why the surface values of the fluxes can be chosen as external parameters. For fluids with large thermal inertia, such as the ocean, the thermal time scale is relatively large, and the density flux is a complex function of depth; thus, the external thermal forcing is no longer a governing parameter. However, the mechanical inertia of the upper ocean is about three orders of magnitude smaller than the thermal inertia. Consequently, the upper ocean can be considered as steady-state in the dynamic sense, to any dynamic property depends primarily on the depth, the surface momentum flux, and the vertical density structure. This property allows us to suggest an alternative formulation of the similarity theory for the stratified boundary layers through specification of a new stratification parameter which characterizes the internal density structure instead of the external density flux. The turbulent mixing coefficient is derived as dependent on the stratification parameter. The latter includes the surface stress and the integral density deficit for the entire layer above. The general form and the asymptotic behavior of the nondimensional turbulent mixing coefficient as a function of the stratification parameter are obtained using dimensional considerations. Determination of numerical parameters is based on 8 years of temperature profiles acquired at the Ocean Weather Ship (OWS) PAPA. Finally, a method for calculating the profile of the turbulent mixing coefficient is obtained. This approach reproduces the 8-year evolution of the upper ocean with the maximum rms difference of approximately 1C and the bias of 1C over the depth range 0–150 m. Additional 1-year simulation of the upper ocean at OWS CHARLEY and 9-year simulation at OWS NOVEMBER confirms reasonable applicability of this approach. The proposed simple turbulent mixing scheme reproduces the evolution of the upper ocean with accuracies similar to those obtained using much more complicated models.