Estimation of maximum scour depths at upstream of front and rear piers for two in-line circular columns

Previous investigations indicate that scour around bridge piers is one of the most important factors for the failure of waterway bridges. Hence, it is essential to determine the accurate scour depth around the bridge piers. Most of the previous studies were based on scour around a single pier; however, in practice, new bridges are usually wide and then piers comprise two circular piers aligned in the flow direction that together support the loading of the structure. In this study, the effect on maximum scour depth of the spacing between two piers aligned in the flow direction was investigated experimentally under clear water scour conditions. The results show that the maximum scour depth at upstream of the front pier occurs when the spacing between the two piers is 2.5 times the diameter of the pier. Two semi empirical equations have been developed to predict the maximum scour depth at upstream of both front and rear piers as a function of the spacing between the piers, in terms of a pier-spacing factor. If the new equations for the pier-spacing factor are used with some of the existing equations for scour at a single pier, the predicted scouring depths are in good agreement with observed results. The S/M equation exhibited the best performance among the various equations tested and was recommended for use in prediction of the equilibrium scour depth. The findings of this study can be used to facilitate the positioning of piers when scouring is a design concern.     

Evaluation of existing equations for temporal scour depth around circular bridge piers

Scour is defined as the processes of removal of sediment particles from water stream bed by the erosive action of activated water, and also carries sediment away from the hydraulic structures. Scour is the main cause of pier failure. Numerous equations are available for estimating temporal and equilibrium scour depth. The present study describes the phenomenon of temporal scour depth variation at bridge piers and deals with the methods for its estimation. The accuracy of six temporal scour depth equations are also checked in this study. After graphical and statistical analysis, it was found that the relationship proposed by Oliveto and Hager (J Hydraul Eng (ASCE) 128(9):811–520, 2002) predicts temporal scour depth better than other equations. Three equations of equilibrium time of scour are also used for computing equilibrium time. Equilibrium time equation proposed by Choi and Choi (Water Environ J 30(1–2):14–21, 2016) gives better agreements with observed values.     

Pier scour within long contraction in cohesive sediment bed

In the present study, an attempt has been made to study the bridge pier scour embedded long contraction for the bed sediment prepared by a mixture of clay and fine sand with varying proportions having a specific range of antecedent moisture content. Results particularly focused on the clay–sand mixed cohesive bed at varying clay fractions of the sediment bed, approach flow velocity, contraction ratio and different pier shapes, on maximum equilibrium scour depth for pier scour within long contraction. Further, regression based equations for the estimation of non-dimensional maximum scour depth for piers within long contraction in clay–sand mixed cohesive bed embedded were proposed.     

Empirical equation for transverse dispersion coefficient based on theoretical background in river bends

There are different approaches to estimating the transverse dispersion coefficient in river mixing. Theoretical approaches have derived the dispersion coefficient from the concept of shear flow, which has dominant effects on the transverse mixing. Empirical approaches have developed an equation using the hydraulic and geometric data of rivers through dimensional analysis and regression techniques. These two equations interact closely with each other. For example, the complicated theoretical equation can be simplified by empirical approaches, and the functional relationships of the empirical equation can be derived from theoretical bases. In this study, a new empirical equation for the transverse dispersion coefficient has been developed based on the theoretical background in river bends. As a regression method, the least-square iterative method was used because the equation was a nonlinear model. The estimated dispersion coefficients derived by the new equation were compared with observed transverse dispersion coefficients acquired from natural rivers and coefficients calculated by the other existing empirical equations. From a comparison of the existing transverse dispersion equations and the proposed equation, it appears that the behavior of the existing formula in a relative sense is very much dependent on the flow condition and the river geometry. Moreover, the proposed equation does not vary widely according to variation of flow conditions. Also, it was revealed that the equation proposed in this study becomes an asymptotic curve as the curvature effect increases.     

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.     

Dressler’s theory for curved topography flows: iterative derivation,transcritical flow solutions and higher-order wave-type equations

The Dressler equations are a system of two non-linear partial differential equations for shallow fluid flows over curved topography. The theory originated from an asymptotic stretching method formulating the equations of motion in terrain-fitted curvilinear coordinates. Apparently, these equations failed to produce a transcritical flow profile changing from sub- to supercritical flow conditions. Further, wave-like motions over a flat bottom are excluded because the bed-normal velocity component is not accounted for. However, the theory was found relevant for several environmental flow problems including density currents over mountains and valleys, seepage flow in hillslope hydrology, the development of antidunes, the formation of geological deposits from hyper-concentrated flows, and shallow-water flow modeling in hydraulics. In this work, Dressler’s theory is developed in an alternative way by a systematic iteration of the stream and potential functions in terrain-fitted coordinates. The first iteration was found to be the former Dressler’s theory, whereas a second iteration of the governing equations results in velocity components generalizing Dressler’s theory to wave-like motion. Dressler’s first-order theory produces a transcritical flow solution over topography only if the total head is fixed by a minimum value of the specific energy at the transition point. However, the theory deviates from measurements under subcritical flow conditions, given that the bed-normal velocity component is significant. A second iteration to the velocity field was used to produce a second-order differential equation that resembles the cnoidal-wave theory. It accurately produces flow over an obstacle including the critical point and the minimum specific energy as part of the numerical solution. The new cnoidal-wave model compares well with the theory of a Cosserat surface for directed fluid sheets, whereas the Saint-Venant theory appears to be poor.     

Numerical simulation of scour around pipelines using an Euler–Euler coupled two-phase model

The scour around a long fixed pipeline placed just above a non-cohesive sandy bed is numerically simulated using an Eulerian two-phase model that implements Euler–Euler coupled governing equations for fluid and solid phases and a modified k−ɛ turbulence closure for the fluid phase, the modeling system being a part of the CFD software package FLUENT. Both flow–particle and particle–particle interactions are considered in the model. During the simulations, the interface between sand and water is specified using a threshold volume fraction of sand, and the evolution of the bedforms is studied in detail. The predictions of bedform evolution are in good agreement with previous laboratory measurements. Investigations into the mechanisms of scour reveal that three sediment transport modes (bed-load, suspended-load and laminated-load) are associated with the scour development. While some previously proposed scour development formulae for cylindrical objects are in good general agreement with the simulations, scour prediction based on a commonly used operational mine-burial model (DRAMBUIE) shows disparities with present simulations.     

A new model for soil–water drainage problems

Seepage flow is an agent related to the transport and dispersion of contamination in groundwater. Steady two-dimensional seepage flow is governed by Laplace’s equation, for which several solution techniques are available. Because computations are complex from a practical point of view, simplified models encompass the Dupuit-Forchheimer approach assuming a horizontal flow. However this approach is inaccurate in seepage problems involving steep drawdowns. In this research, a new theoretical model for 2D seepage flow is proposed based on Fawer’s theory for curved flows Castro-Orgaz (Environ Fluid Mech 10(3):2971–2310, 2010), from which a second-order equation results describing the seepage surface. From this development, a numerical solution for the rectangular dam problem based on the second-order model is presented, whereas a simple first-order equation is found to describe flow to drains under a uniform rainfall. The results of this new model are compared with the full 2D solution of Laplace’s equation for typical test cases, resulting in an excellent agreement.     

Prediction of mass and momentum transport in turbulent plane wall jets over smooth and transitionally rough surfaces

This paper is concerned with the prediction of mass and momentum transport in turbulent wall jets developing over smooth and transitionally rough plane walls. The ability to accurately predict the resulting wall shear stresses and vertical profiles of the Reynolds stresses in these flows is prerequisite to the accurate prediction of bed scour, sediment re-suspension and transport by turbulent diffusion. The computations were performed by solving the Reynolds-averaged forms of the equations describing conservation of mass, momentum and concentration. The unknown correlations that arise from the averaging process (the Reynolds stresses in the case of the momentum equation, and the turbulent mass fluxes in the case of concentration) were obtained from the solution of modeled differential equations that describe their conservation. Since these models are somewhat more complex than those typically used in practice, their benefits are demonstrated by comparisons with results obtained from simpler, eddy-viscosity based closures. Comparisons with experimental data show that results of acceptable accuracy can be obtained only by using the appropriate combination of models for the turbulent fluxes of mass and momentum that properly account for the reduction of the Reynolds stresses due to wall damping effects, and for the modification of the mass transfer rates due to interactions with the mean rates of strain.     

Impulsive waves caused by subaerial landslides

This paper presents the experimental results of impulsive waves caused by subaerial landslides. A wide range of effective parameters are considered and studied by performing 120 laboratory tests. Considered slide masses are both rigid and deformable. The effects of bed slope angle, water depth, slide impact velocity, geometry, shape and deformation on impulse wave characteristics have been inspected. The impulse wave features such as amplitude, period and also energy conversation are studied. The effects of slide Froude number and deformation on energy conversation from slide into wave are also investigated. Based on laboratory measured data an empirical equation for impulse wave amplitude and period have been presented and successfully verified using available data of previous laboratory works.     

Spreading of oil on water in the surface-tension regime

The third stage of oil spreading on water, in which surface-tension force promotes spreading against the resisting viscous effect, is investigated using a similarity solution in combination with an integral boundary-layer technique to solve the unidirectional oil-spreading dynamics problem in the last stage of spreading. The thin layer is assumed to be supplied by oil from a bulk boundary. Using a constitutive equation for oil-film surface tension versus oil-film thickness, analytical solutions near the bulk boundary and near the edge are developed. Using the asymptotic solutions to initiate integration, the differential equations for the oil thickness, oil velocity, and boundary-layer profiles are integrated starting from the leading edge and bulk boundary, which after matching provide a complete solution. The results for the spreading-law prefactors are found to differ by about 10 % from published theoretical results using the same constitutive equation. Using an empirical constitutive equation for oil-film surface tension versus distance from the bulk boundary leads to a spreading-law prefactor that is in excellent agreement with the published experimental result and published theoretical work providing and using the same empirical constitutive equation.     

氮沉降增加对土壤微生物的影响

综述了国外氮沉降对土壤微生物的影响研究现状，主要从土壤微生物群落结构组成及功能等方面对氮沉降的响应进行了综述，并从微生物对底物的利用模式及碳分配状况，pH值的变化方面初步探讨了土壤微生物对过量氮沉降的响应机制。研究表明，过量氮沉降会给土壤微生物在以下几个方面带来负影响：首先，改变微生物群落结构组成，表现为土壤真菌细菌相关丰富度发生改变，真菌生物量的减少，真菌／细菌生物量比率的减少，土壤微生物量的减少，微生物群落结构发生改变；其次，改变微生物功能，表现为减少土壤呼吸率，土壤酶活性的降低，改变微生物对底物的利用模式等等。此外，文章还指出出未来该方面研究重点和方向。     

Development of an empirical equation for the transverse dispersion coefficient in natural streams

In this study, a new empirical equation for the transverse dispersion coefficient has been developed based on the hydraulic and geometric parameters in natural streams using a regression technique. First, a total of 32 data sets in 16 streams were collected. Among those sets, 16 sets were used for deriving the new equation, and the other 16 sets were used for verifying the equation. Then, through dimensional analysis, it was found that the normalized transverse dispersion coefficient is associated with several parameters such as sinuosity, aspect ratio, and a friction term. The robust least square method was applied to estimate regression coefficients. The newly proposed equation was proven to be superior in explaining the dispersion characteristics of natural streams more precisely compared to the existing equations.     

Comments on “Development of an empirical equation for the transverse dispersion coefficient in natural streams” by Tae Myoung Jeon,Kyong Oh Baek and Il Won Seo

In a recent paper published in this journal, Jeon et al. ((2007), Environ Fluid Mech 7(4): 317–329) have presented a new empirical equation for the transverse dispersion coefficient in natural streams that was developed based on the hydraulic and geometric parameters using a regression technique. A total of 32 data sets collected in 32 streams was used. Among them, 16 data sets were used for deriving the new equation, and the other 16 were used for verifying the equation. Starting from dimensional analysis the authors found that transverse dispersion coefficient depends on three parameters, such as sinuosity, aspect ratio and a friction term. The robust least square method was applied to estimate regression coefficients resulting in an equation which allows better prediction of transverse dispersion coefficient than previous literature equations. The discussers would like to highlight some points raised in the paper.     

Empirical modeling of atmospheric deposition in mountainous landscapes.

Atmospheric deposition has long been recognized as an important source of pollutants and nutrients to ecosystems. The need for reliable, spatially explicit estimates of total atmospheric deposition (wet + dry + cloud) is central, not only to air pollution effects researchers, but also for calculation of input-output budgets, and to decision makers faced with the challenge of assessing the efficacy of policy initiatives related to deposition. Although atmospheric deposition continues to represent a critical environmental and scientific issue, current estimates of total deposition have large uncertainties, particularly across heterogeneous landscapes such as montane regions. We developed an empirical modeling approach that predicts total deposition as a function of landscape features. We measured indices of total deposition to the landscapes of Acadia (121 km2) and Great Smoky Mountains (2074 km2) National Parks (USA). Using approximately 300-400 point measurements and corresponding landscape variables at each park, we constructed a statistical (general linear) model relating the deposition index to landscape variables measured in the field. The deposition indices ranged over an order of magnitude, and in response to vegetation type and elevation, which together explained approximately 40% of the variation in deposition. Then, using the independent landscape variables available in GIS data layers, we created a GIS-relevant statistical nitrogen (N) and sulfur (S) deposition model (LandMod). We applied this model to create park-wide maps of total deposition that were scaled to wet and dry deposition data from the closest national network monitoring stations. The resultant deposition maps showed high spatial heterogeneity and a four- to sixfold variation in "hot spots" and "cold spots" of N and S deposition ranging from 3 to 31 kg N x ha(-1) x yr(-1) and from 5 to 42 kg S x ha(-1) x yr(-1) across these park landscapes. Area-weighted deposition was found to be up to 70% greater than NADP plus CASTNET monitoring-station estimates together. Model-validation results suggest that the model slightly overestimates deposition for deciduous and coniferous forests at low elevation and underestimates deposition for high-elevation coniferous forests. The spatially explicit deposition estimates derived from LandMod are an improvement over what is currently available. Future research should test LandMod in other mountainous environments and refine it to account for (currently) unexplained variation in deposition.     

A kinetic approach to the aerobic sediment-water exchange of phosphorus in Lake Esrom

An empirical equation for the temperature-dependent sediment-water exchange of phosphorus, describing exchange as the sum of desorption, diffusion and biological degradation processes, is derived from previous experiments and observed temperature-exchange relationships. Additional equations for littoral and profundal exchange rates are developed. Calculated exchange values are compared with observed exchange values and the ratio: nitrogen released/phosphorus released compared with the sedimentation of phosphorus.     

Seed terminal velocity, wind turbulence, and demography drive the spread of an invasive tree in an analytical model

Little is known about the relative importance of mechanistic drivers of plant spread, particularly when long-distance dispersal (LDD) events occur. Most methods to date approach LDD phenomenologically, and all mechanistic models, with one exception, have been implemented through simulation. Furthermore, the few recent mechanistically derived spread models have examined the relative role of different dispersal parameters using simulations, and a formal analytical approach has not yet been implemented. Here we incorporate an analytical mechanistic wind dispersal model (WALD) into a demographic matrix model within an analytical integrodifference equation spread model. We carry out analytical perturbation analysis on the combined model to determine the relative effects of dispersal and demographic traits and wind statistics on the spread of an invasive tree. Models are parameterized using data collected in situ and tested using independent data on historical spread. Predicted spread rates and direction match well the two historical phases of observed spread. Seed terminal velocity has the greatest potential influence on spread rate, and three wind properties (turbulence coefficient, mean horizontal wind speed, and standard deviation of vertical wind speed) are also important. Fecundity has marginal importance for spread rate, but juvenile survival and establishment are consistently important. This coupled empirical/theoretical framework enables prediction of plant spread rate and direction using fundamental dispersal and demographic parameters and identifies the traits and environmental conditions that facilitate spread. The development of an analytical perturbation analysis for a mechanistic spread model will enable multispecies comparative studies to be easily implemented in the future.     

Dominant features in three-dimensional turbulence structure: comparison of non-uniform accelerating and decelerating flows

The results are presented from an experimental study to investigate three-dimensional turbulence structure profiles, including turbulence intensity and Reynolds stress, of different non-uniform open channel flows over smooth bed in subcritical flow regime. In the analysis, the uniform flow profiles have been used to compare with those of the non-uniform flows to investigate their time-averaged spatial flow turbulence structure characteristics. The measured non-uniform velocity profiles are used to verify the von Karman constant κ and to estimate sets of log-law integration constant B_r and wake parameter П, where their findings are also compared with values from previous studies. From κ, B_r and П findings, it has been found that the log-wake law can sufficiently represent the non-uniform flow in its non-modified form, and all κ, B_r and П follow universal rules for different bed roughness conditions. The non-uniform flow experiments also show that both the turbulence intensity and Reynolds stress are governed well by exponential pressure gradient parameter β equations. Their exponential constants are described by quadratic functions in the investigated β range. Through this experimental study, it has been observed that the decelerating flow shows higher empirical constants, in both the turbulence intensity and Reynolds stress compared to the accelerating flow. The decelerating flow also has stronger dominance to determine the flow non-uniformity, because it presents higher Reynolds stress profile than uniform flow, whereas the accelerating flow does not.     

Testing Accuracy of Finite Element and Random Walk Schemes in Prediction of Pollutant Dispersion in Coastal Waters

Distribution of pollutants in coastal waters is usually represented by depth averaged twodimensional convection-dispersion equation. Under very specific conditions this equation can be solved analytically. Although such a solution is restricted to simplified situations it provides a very useful case for testing the performance of various numerical solution techniques currently available for the simulation of convective-dispersion of pollutants in natural water systems. In this paper the analytical solution of the convective dispersion equation is used as a benchmark against which the accuracy of other techniques are assessed. These assessments are based on quantitative comparisons between the results of the solution of two-dimensional convection-dispersion equation by the deterministic finite element and stochastic random walk methods. Both Eulerian and Lagrangian frameworks are employed to obtain the finite element solution of the convection-dispersion problem. It has been shown that the Lagrange–Galerkin finite element scheme yields the most accurate results for the case under study. However, computational costs of the Lagrange–Galerkin method can be relatively high and under certain conditions it may be reasonable to use a less accurate but cost effective random walk scheme to make water quality management decisions.     

Response of predators to loss and fragmentation of prey habitat: a review of theory

Despite extensive empirical research and previous reviews, no clear patterns regarding the effects of habitat loss and fragmentation on predator-prey interactions have emerged. We suggest that this is because empirical researchers do not design their studies to test specific hypotheses arising from the theoretical literature. In fact, theoretical work is almost completely ignored by empirical researchers, perhaps because it may be inaccessible to them. The purpose of this paper is to review theoretical work on the effects of habitat loss and fragmentation on predator-prey interactions. We provide a summary of clear, testable theoretical predictions for empirical researchers. To test one or more of these predictions, an empiricist will need certain information on the predator and prey species of interest. This includes: (1) whether the predator is a specialist on one prey species or feeds on many kinds of prey (omnivore and generalist); (2) whether the predator is restricted to the same habitat type as the focal prey (specialist), can use a variety of habitats but has higher survival in the prey habitat (omnivore), or lives primarily outside of the focal prey's habitat (generalist); (3) whether prey-only patches have lower prey extinction rates than predator-prey patches; and (4) whether the prey emigrate at higher rates from predator-prey patches than from prey-only patches. Empiricists also need to be clear on whether they are testing a prediction about habitat loss or habitat fragmentation and need to conduct empirical studies at spatial scales appropriate for testing the theoretical prediction(s). We suggest that appropriate use of the theoretical predictions in future empirical research will resolve the apparent inconsistencies in the empirical literature on this topic.