Mass-based depth and velocity scales for gravity currents and related flows

Gravity driven flows on inclines can be caused by cold, saline or turbid inflows into water bodies. Another example are cold downslope winds, which are caused by cooling of the atmosphere at the lower boundary. In a well-known contribution, Ellison and Turner (ET) investigated such flows by making use of earlier work on free shear flows by Morton, Taylor and Turner (MTT). Their entrainment relation is compared here with a spread relation based on a diffusion model for jets by Prandtl. This diffusion approach is suitable for forced plumes on an incline, but only when the channel topography is uniform, and the flow remains supercritical. A second aspect considered here is that the structure of ET’s entrainment relation, and their shallow water equations, agrees with the one for open channel flows, but their depth and velocity scales are those for free shear flows, and derived from the velocity field. Conversely, the depth of an open channel flow is the vertical extent of the excess mass of the liquid phase, and the average velocity is the (known) discharge divided by the depth. As an alternative to ET’s parameterization, two sets of flow scales similar to those of open channel flows are outlined for gravity currents in unstratified environments. The common feature of the two sets is that the velocity scale is derived by dividing the buoyancy flux by the excess pressure at the bottom. The difference between them is the way the volume flux is accounted for, which—unlike in open channel flows—generally increases in the streamwise direction. The relations between the three sets of scales are established here for gravity currents by allowing for a constant co-flow in the upper layer. The actual ratios of the three width, velocity, and buoyancy scales are evaluated from available experimental data on gravity currents, and from field data on katabatic winds. A corresponding study for free shear flows is referred to. Finally, a comparison of mass-based scales with a number of other flow scales is carried out for available data on a two-layer flow over an obstacle. Mass-based flow scales can also be used for other types of flows, such as self-aerated flows on spillways, water jets in air, or bubble plumes.     

Flow structure and turbulence characteristics downstream of a spanwise suspended linear array

Laboratory experiments are conducted to quantify the mean flow structure and turbulence properties downstream of a spanwise suspended linear array in a uniform ambient water flow using Particle Tracking Velocimetry. Eighteen experimental scenarios, with four depth ratios (array depth to water column depth) of 0.35, 0.52, 0.78, and 0.95 and bulk Reynolds number (length scale is the array depth) from 11,600 to 68,170, are investigated. Three sub-layers form downstream of the array: (1) an internal wake zone, where the time-averaged velocity decreases with increasing distance downstream, (2) a shear layer which increases in vertical extent with increasing distance downstream of the array, and the rate of the increase is independent of the bulk Reynolds number or the depth ratio, and (3) an external wake layer with enhanced velocity under the array. The location of the shear layer is dependent on the depth ratio. The spatially averaged and normalized TKE of the wake has a short production region, followed by a decay region which is comparable to grid turbulence decay and is dependent on the depth ratio. The results suggest that the shear layer increases the transfer of horizontal momentum into the internal wake zone from the fluid outside of the array and that the turbulence in the internal wake zone can be modeled similarly to that of grid turbulence.     

3D model for a secondary facultative pond

This paper describes a comprehensive model of wastewater treatment in secondary facultative ponds, which combines 3D hydrodynamics with a mechanistic water quality model. The hydrodynamics are based on the Navier-Stokes equation for incompressible fluids under shallow water and Boussinesq assumptions capturing the flow dynamics along length, breadth and depth of the pond. The water quality sub model is based on the Activated Sludge Model (ASM) concept, describing COD and nutrient removal as function of bacterial growth following Monod kinetics, except for Escherichia coli removal, which was modelled as first order decay. The model was implemented in the Delft3D software and was used to evaluate the effect of wind and the addition of baffles on the water flow pattern, temperature profiles in the pond and treatment efficiency. In contrast to earlier models reported in the literature, our simulation results did not show any significant improvement in COD removal (based on the ASM concept) with addition of baffles or under intermittent wind-induced mixing. However, E. coli removal efficiency, based on a first order decay approach, showed a fair improvement in the presence of baffles or intermittent wind-induced mixing. Furthermore, simulations with continuous wind effect showed a decrease in removal efficiency for COD but a further increase in E. coli removal efficiency. Such contrasting results for two different approaches in modelling could indicate that the first order decay concept might not be appropriate to describe all the interactions between biochemical processes in a pond. However, these interpretations remain theoretical, as the model needs validation with field data.     

Modeling and verifying chlorine decay and chloroacetic acid formation in drinking water chlorination

This study presents a phenomenological model that can be used by the water professionals to quantify chlorine decay and disinfection byproduct (DBP) formation in water. The kinetic model was developed by introducing the concept of limiting chlorine demand and extending an established reactive species approach. The limiting chlorine demand, which quantifies chlorine reactive natural organic matter (NOM) on an equivalent basis, was mathematically defined by the relation between ultimate chlorine residue and initial chlorine dose. It was found experimentally that NOM in water has limiting chlorine demand that increases with chlorine dose once the ultimate residue is established. These results indicated that the complex NOM has a unique ability to adjust chemically to the change in redox condition caused by the free chlorine. It is attributed mainly to the redundant functional groups that persist in heterogeneous NOM molecules. The results also demonstrated that the effect of chlorine dose on the rate of chlorine decay can be quantitatively interpreted with the limiting chlorine demand. The kinetic model developed was validated for chlorine decay and chloroacetic acid formation in finished drinking water.     

Effect of pollutant decay on steady-state concentration distributions in variable depth flow

Pollutants discharged together in a variable-depth flow can separate laterally if the decay mechanisms differ e.g. evaporation is more effective in shallow water, but floc breakup is more effective in deeper faster flow. Ray tracing of concentration information away from a point source (similar to mathematical optics) is used to quantify the effects of decay. The concentration reduction rate along a ray increases with decay rate divided by flow speed and with angle between the flow and information directions. Pollutant concentrations tend to fractionate towards regions of smaller decay rate divided by flow speed.     

Local calibration of coliforms parameters of water quality problem at Igapó I Lake, Londrina, Paraná, Brazil

This article presents results concerning the local calibration of the transport parameters (longitudinal and transversal diffusions and decay coefficient) for a two-dimensional problem of water quality at Igapó I Lake, located in Londrina, Paraná, Brazil, using fecal coliforms as an indicator of water quality. The simulation of fecal coliforms concentrations all over the water body is conducted by means of a structured discretization of the geometry of Igapó I Lake, together with the finite difference and finite element methods. By using the velocity field, modeled by the Navier-Stokes and Poisson equations, the flow of fecal coliforms is described by means of a transport model, which considers advective and diffusive processes, as well as a process of fecal coliforms decay. In the checkpoint, the longitudinal and transversal diffusion coefficients and the coliforms decay coefficient that best fitted the value of the fecal coliforms concentration were D_x = D_y = 0.001 m²/h and k = 0.5 d⁻¹ = 0.02083 h⁻¹. A qualitative and quantitative analysis of the numerical simulations conducted in function of the diffusion coefficients and of the coliforms decay parameter provided a better understanding of the local water quality at Igapó I Lake.     

Monitoring and estimating the flow conditions and fish presence probability under various flow conditions at reach scale using genetic algorithms and kriging methods

The combination of current velocity and water depth influences stream flow conditions, and fish activities prefer particular flow conditions. This study develops a novel optimal flow classification method for identifying types of stream flow based on the current velocity and the water depth using a genetic algorithm. It is applied to the Datuan stream in northern Taiwan. Fish were sampled and their habitat investigated at the study site during the spring, summer, fall and winter of 2008-2009. The current velocity, water depth and maps of the presence probability of fish were estimated by ordinary and indicator kriging. The optimal classification results were compared with the classification results obtained using the Froude number and empirical methods. The flow classification results demonstrate that the proposed optimal flow classification method that considers depth-velocity and optimally identified criteria for classifying flow types, yields a current velocity and water depth of 0.32 (m/s) and 0.29 (m), respectively, and classifies the flow conditions in the study area as pool, run, riffle and slack. The variography results of the current velocity and the water depth data reveal that seasonal flows are not spatially stationary among seasons in the study area. Kriging methods and a two-dimensional hydrodynamic model (River 2D) with empirical and optimal flow classification methods are more effective than the Froude number method in classifying flow conditions in the study area. The flow condition classifications and probability maps were generated by River 2D, ordinary kriging and indicator kriging, to quantify the flow conditions preferred by Sicyopterus japonicus in the study area. However, the proposed optimal classification method with kriging and River 2D is an effective alternative method for mapping flow conditions and determining the relationship between flow and the presence probability of target fish in support of stream restoration.     

Modeling the buoyant flow of heated water discharged from surface and submerged side outfalls in shallow and deep water with a cross flow

In this study, a three-dimensional model was used to numerically study the buoyant flow, along with its mixing characteristics, of heated water discharged from the surface and submerged side outfalls in shallow and deep water with a cross flow. Hydraulic experimental data were used to evaluate the applicability of the model. The simulation results agree well with the experimental results, particularly, the jet trajectories, the dimensions of the recirculating zone, and the distribution of the dimensionless excess temperature. The level of accuracy of the simulation results of the present study is nearly identical to that of the results conducted by McGuirk and Rodi (1978). If the heated water is discharged into shallow water where the momentum flux ratio and the discharge densimetric Froude number are high, the submerged discharge method is better than the surface discharge method in terms of the scale of the recirculating zone and the minimum dilution. In deep water, where the momentum flux ratio and discharge densimetric Froude number are low, however, the submerged discharge method had few advantages. In shallow water, the discharge jet is deflected by the ambient cross flow, while forcing the ambient flow to bend towards the far bank for the full depth. For a submerged discharge in shallow water, the recirculating zone is the largest in the lowest layer but becomes smaller in the upper layer. As the water depth increases, the ambient flow goes over the jet and diminishes the blocking effect, thereby decreasing the bending of the jet.     

Vertical migration strategies with respect to advection and stratification in a semi-enclosed lough: a comparison of mero- and holozooplankton

Patterns of zooplankton vertical movement are often difficult to interpret because of multiple, complex and confounding environmental factors. Behavioural adaptations to these environmental variables are compared within and between the holo- and meroplankton constituents of a community. We used a nested design to analyse patterns at several scales in time; (semi-diel, diel, spring-neap tidal cycle and season) and two in space; (depth and site). To reduce complexity and aid interpretation we studied a semi-isolated community in a semi-enclosed, seasonally stratified sea lough (Lough Hyne Marine Nature Reserve, Ireland). In this, the main environmental gradient was water flow rate (or water residence time) caused by tidal currents. Vertical profiles of abundance showed that populations of the most abundant species of holo- and meroplankton in the lough have considerable behavioural plasticity, enabling them to switch between sedentary and migratory behaviour and patterns of migration. Some species migrate vertically in synchrony with diel cycles and others in response to semi-diel tidal currents; a few do both, but the majority did neither. It is suggested that water column structure and hydrographic discontinuities caused by flow rate and pycnocline dynamics are responsible for the variable patterns of vertical migration and distribution.Communicated by J.P. Thorpe, Port Erin     

洞庭湖封闭河口区与湖心区的基本生态特征——以六门闸至小西湖样带为例

通过对洞庭湖六门闸至小西湖样带的调查,研究了封闭河口区和湖心区水体、土壤和植物等基本生态特征及其相关关系。结果表明,河口区水流缓慢,透明度低,而湖心区水流速度较高,透明度也高;河口区水体具有较高的营养水平和电导率,而湖心区水体营养水平和电导率相对较低;湖心区土壤有机质和氮含量较高,而河口区有机质和氮含量相对较低;河口区不适合水生植物的生长繁殖,而湖心区是植物生长繁殖的主要生境。相关分析结果表明,河口区和湖心区生物、土壤和水文特征之间存在相互作用,透明度与水流速度之间在α=0.05水平上相关显著,物种丰富度、生物量和多样性指数分别与水流速度和透明度在α=0.01水平上相关显著,与土壤全氮含量之间在α=0.05水平上相关显著,水流速度是调控生态特征变化的关键因子。     

Experimental investigation of bubbly flow and turbulence in hydraulic jumps

Many environmental problems are linked to multiphase flows encompassing ecological issues, chemical processes and mixing or diffusion, with applications in different engineering fields. The transition from a supercritical flow to a subcritical motion constitutes a hydraulic jump. This flow regime is characterised by strong interactions between turbulence, free surface and air–water mixing. Although a hydraulic jump contributes to some dissipation of the flow kinetic energy, it is also associated with increases of turbulent shear stresses and the development of turbulent eddies with implications in terms of scour, erosion and sediment transport. Despite a number of experimental, theoretical and numerical studies, there is a lack of knowledge concerning the physical mechanisms involved in the diffusion and air–water mixing processes within hydraulic jumps, as well as on the interaction between the free-surface and turbulence. New experimental investigations were undertaken in hydraulic jumps with Froude numbers up to Fr = 8.3. Two-phase flow measurements were performed with phase-detection conductivity probes. Basic results related to the distributions of void fraction, bubble frequency and mean bubble chord length are presented. New developments are discussed for the interfacial bubble velocities and their fluctuations, characterizing the turbulence level and integral time scales of turbulence representing a “lifetime” of the longitudinal bubbly flow structures. The analyses show good agreement with previous studies in terms of the vertical profiles of void fraction, bubble frequency and mean bubble chord length. The dimensionless distributions of interfacial velocities compared favourably with wall-jet equations. Measurements showed high turbulence levels. Turbulence time scales were found to be dependent on the distance downstream of the toe as well as on the distance to the bottom showing the importance of the lower (channel bed) and upper (free surface) boundary conditions on the turbulence structure.     

Model of turbulence penetration into a suspension layer on a sediment bed and effect on vertical solute transfer

The vertical diffusional mass (solute) transfer through a suspended sediment layer, e.g. at the bottom of a lake, reservoir or estuary, by the propagation of velocity fluctuations from above was investigated. The attenuation of the velocity fluctuations in the suspension layer and the associated effect on solute transfer through the suspension layer was simulated. To represent large eddies traveling downstream in water over a high-concentration suspended sediment layer, a streamwise velocity fluctuation moving in downstream direction was imposed along the upper boundary of the suspension layer. Velocity fluctuations and downstream velocity were normalized by the shearvelocity (U_*) at the top of the suspension layer. Streamwise and vertical velocity components inside the suspension layer, were obtained from the 2-D continuity and the Navier–Stokes equations. The persistence of turbulence with depth—as it penetrates from the overlying water into the suspension layer—was found to depend on its amplitude, its period, and on the apparent viscosity of the suspension. The turbulence was found to propagate efficiently into the suspension layer when its frequency is low, and the apparent viscosity of the suspension is high. Effects on vertical mass transfer were parameterized by penetration depth and effective diffusion coefficient, and related to apparent viscosity of the suspension, Schmidt number and shear velocity on top of the suspension layer. The enhancement of turbulence penetration by viscosity is similar to the flow near an oscillating flat plate (Stokes’ second problem), but is opposite to turbulence penetration into a stationary porous and permeable sediment bed. The information is applicable to water quality modeling mear the sediment/water interface of lakes, river impoundments and estuaries.     

The wave-induced solute flux from submerged sediment

The issue of the transport of dissolved nutrients and contaminants between the sediment in the bottom of a lake or reservoir and the body of water above it is an important one for many reasons. In particular the biological and chemical condition of the body of water is intricately linked to these mass transport processes. As the review by Boudreau (Rev Geophys 38(3):389–416, 2000) clearly demonstrates those transport processes are very complex involving mechanisms as diverse as the wave-induced flux between the sediment and the overlying water and the effect of burrowing animals on the transport within the sediment as well as basic diffusion mechanisms. The present paper focuses on one facet of these transport processes; we re-examine the balance of diffusion and wave-induced advection and demonstrate that the wave-induced flux of a solute from submerged sediment is not necessarily purely diffusive as suggested by Harrison et al. (J Geophys Res 88:7617–7622, 1983) but can be dominated by a mean or time-averaged flux induced by the advective fluid motion into and out of the sediment caused by the fluctuating pressure waves associated with wave motion. Indeed along the subtidal shoreline where the fluctuating bottom pressures are greatest, wave-induced advection will dominate the mean, time-averaged transport of solute into or out of the sediment as suggested in the work of Riedl et al. (Mar Biol 13:210–221, 1972). However, the present calculations also indicate that this advective flux decreases rapidly with increasing depth so that further away from the shoreline the advective flux becomes negligible relative to the diffusive flux and therefore the latter dominates in deeper water.     

Circulation of perivisceral fluid in the sea urchin Lytechinus variegatus

The principal driving mechanism of perivisceral-fluid circulation was investigated in the echinoid Lytechinus variegatus by metal-clad hot-wire anemometry. Analysis of 23 flow profiles from 13 individuals collected from 1 to 3 m water depth at Tarpon Springs and Sarasota, Florida (USA) in 1984 indicates that for this species, the ciliated epithelium is an ineffective driving mechanism for mixing of the perivisceral fluid. Instead, the Aristotle's lantern is the major driving force of circulation of the perivisceral fluid, with velocity fluctuations of 1.5 mm s^-1 amplitude in the cavity center during intermittent periods of activity. These fluctuations rapidly decay as the ciliated surfaces are approached. Spectral analysis of velocity time-series reveals predominant energy-containing velocity fluctuations between 0.007 and 0.05 Hz. The circulation, which can be described as non-turbulent forced mixing, has revealed four different flow patterns which appear to be correlated with specific animal activities. A modified eddydiffusion model predicts that oxygen transport through the cavity over a 2 cm path length requires more than 20 h. Calculation of the oxygen flux to a ripe ovary suggests that supply does not meet ovarian oxygen demand in this case. Alternative pathways of oxygen transport invoking advection in perivisceral-fluid eddies and along the ciliated coelomic surfaces are compatible with the observed flow patterns and lead to much shorter oxygen-transport time scales of the order of 1 to 10 min.     

Dissipation of Tidal Energy and Associated Mixing in a Wide Fjord

This paper sets out to test the hypothesis that vertical mixing due to the dissipation of the internal tide accounts for a significant proportion of the total vertical mixing in a fjordic basin during a period of deep water isolation. During July and August 1999 two locations in the Clyde Sea were instrumented with moored RD Instruments Acoustic Doppler Current Profilers (ADCPs) and conductivity-temperature-pressure chains: Station C2, near the shallow entrance sill (55 m water depth), and station C1 in the deep basin (155 m water depth). A bottom pressure recorder was also deployed at station C3 by the seaward entrance to the Clyde Sea in the North Channel of the Irish Sea. A Free-falling Light Yo-yo shear microstructure profiler (FLY) was used to measure the dissipation rate of turbulent kinetic energy (TKE) throughout the water column over 25 h at both C1 and C2. These were interspersed with two-hourly conductivity-temperature-depth casts at both sites. The observations show agreement between the dissipation rate of TKE estimated by using a microstructure profiler and that estimated from the decay of the internal tide as measured by the two ADCPs. However, to account for all the implied mixing it is necessary to invoke an additional source of buoyancy flux, the most probable candidate mechanism is enhanced internal wave breaking near the sill and at the sloping boundaries of the deep basin. In addition, the vertical eddy diffusivity estimated from the micro-structure profiler (O(0.5 cm² s^–1) indicates that internal tide induced mixing away from any boundaries contributed significantly to the overall level of mixing which is required to account for the observed evolution of the deep basin water properties.     

Mobility of free surface in different liquids and its influence on water striders locomotion

Dynamics of the surface layer in different liquids is examined by means of infrared thermography of the surface and simultaneous velocity fields measurements using surface and infrared Particle Image Velocimetry. This technique allows measurements and comparison of two velocity fields—at the surface and at small depth about 50–200 μm. In distilled water the velocity fields at the surface and at small depth exhibit significant dissimilarity. The flow field below the surface is essentially 3D, whereas the surface flow is characterized by vanishing 2D divergence of velocity, indicating predominantly planar motion. In contrast, in ethanol–butanol mixture two velocity fields are well correlated, both corresponding to 3D flow with continuous surface renewal. Thermal patterns, observed at the surface, and the flow field structure in different liquids are associated with different boundary conditions for velocity at the surface. Water surface is seldom renewed, which inhibits heat and mass exchange between the liquid and atmosphere. However, absence of vertical advection also enables organisms to live within the surface layer, to stand and walk on the free surface. This is illustrated by the difficulties a water strider faces on the surface of ultrapure water, which exhibits Marangoni convection.     

Simulation of water quality in a flood detention area using models of different spatial discretization

Detention areas provide a means to lower peak discharges in rivers by temporarily storing excess water. In the case of extreme flood events, the storage effect reduces the risk of dike failures or extensive inundations for downstream reaches and near the site of abstraction. Due to the large amount of organic matter contained in the river water and the inundation of terrestrial vegetation in the detention area, a deterioration of water quality may occur. In particular, decay processes can cause a severe depletion of dissolved oxygen (DO) in the temporary water body. In this paper, we studied the potential of a water quality model to simulate the DO dynamics in a large but shallow detention area to be built at the Elbe River (Germany). Our focus was on examining the impact of spatial discretization on the model’s performance and usability. Therefore, we used a zero-dimensional (0D) and a two-dimensional (2D) modeling approach in parallel. The two approaches solely differ in their spatial discretization, while conversion processes, parameters, and boundary conditions were kept identical. The dynamics of DO simulated by the two models are similar in the initial flooding period but diverge when the system starts to drain. The deviation can be attributed to the different spatial discretization of the two models, leading to different estimates of flow velocities and water depths. Only the 2D model can account for the impact of spatial variability on the evolution of state variables. However, its application requires high efforts for pre- and post-processing and significantly longer computation times. The 2D model is, therefore, not suitable for investigating various flood scenarios or for analyzing the impact of parameter uncertainty. For practical applications, we recommend to firstly set up a fast-running model of reduced spatial discretization, e.g. a 0D model. Using this tool, the reliability of the simulation results should be checked by analyzing the parameter uncertainty of the water quality model. A particular focus may be on those parameters that are spatially variable and, therefore, believed to be better represented in a 2D approach. The benefit from the application of the more costly 2D model should be assessed, based on the analyses carried out with the 0D model. A 2D model appears to be preferable only if the simulated detention area has a complex topography, flow velocities are highly variable in space, and the parameters of the water quality model are well known.     

A submodel for anaerobic mud-water exchange of phosphate

A submodel for anaerobic mud-water exchange of phosphate is obtained from experiments in the laboratory. Phosphorus in the sediment can be divided into exchangeable and non-exchangeable phosphorus. The exchangeable phosphorus is decomposed in accordance with a first-order reaction. The phosphorus moves, after the decomposition process, from the interstitial water to the water phase, in accordance with a diffusion expression. The yearly increase of the sediment was determined by means of the lead concentration as a function of the depth.