Advances in Environmental Fluid Mechanics

The following sections are included:

• Preface

• Biographies of Editors and Contributors

• Contents

We consider the dispersion of contaminants in turbulent flows at high Péclet number. Except at the smallest scales, molecular diffusion acts slowly by comparison with turbulent advection. Molecular diffusion is still important because it is the only means by which the concentration in a fluid particle can be changed. Exact solution of the full problem, including both turbulent advection and molecular diffusion, is not possible because of the well-known turbulence closure problem. But exact results for moments and the probability density function (pdf) of concentration can be derived for the hypothetical case of zero diffusivity. For high Péclet number these results can be expected to hold in certain ranges of space and time with only slight modification. We outline the results in the absence of molecular diffusion, and consider how the results for the moments can be modified to account for the presence of slowly acting diffusion. The model expressions for the moments involve the mean concentration, and a set of parameters which vary slowly with distance from the source, or with time since release. The corresponding form of the pdf is considered, and results for large concentrations are presented. It is shown that many of the results obtained with this approach agree well with experimental observations. Areas needing further work are also suggested.

The field of environmental sciences is abundant with various interfaces and is the right place for the application of new fundamental approaches leading towards a better understanding of environmental phenomena. For example, following the definition of environmental interface by Mihailovic and Balaž [23], such interface can be placed between: human or animal bodies and surrounding air, aquatic species and water and air around them, and natural or artificially built surfaces (vegetation, ice, snow, barren soil, water, urban communities) and the atmosphere. Complex environmental interface systems are open and hierarchically organised, interactions between their constituent parts are nonlinear, and the interaction with the surrounding environment is noisy. These systems are therefore very sensitive to initial conditions, deterministic external perturbations and random fluctuations always present in nature. The study of noisy non-equilibrium processes is fundamental for modelling the dynamics of environmental interface systems and for understanding the mechanisms of spatio-temporal pattern formation in contemporary environmental sciences, particularly in environmental fluid mechanics. In modelling complex biophysical systems one of the main tasks is to successfully create an operative interface with the external environment. It should provide a robust and prompt translation of the vast diversity of external physical and/or chemical changes into a set of signals, which are “understandable” for an organism. Although the establishment of organisation in any system is of crucial importance for its functioning, it should not be forgotten that in biophysical systems we deal with real-life problems where a number of other conditions should be reached in order to put the system to work. One of them is the proper supply of the system by the energy. Therefore, we will investigate an aspect of dynamics of energy flow based on the energy balance equation. The energy as well as the exchange of biological, chemical and other physical quantities between interacting environmental interfaces can be represented by coupled maps. In this chapter we will address only two illustrative issues important for the modelling of interacting environmental interfaces regarded as complex systems. These are (i) use of algebra for modelling the autonomous establishment of local hierarchies in biophysical systems and (ii) numerical investigation of coupled maps representing exchange of energy, chemical and other relevant biophysical quantities between biophysical entities in their surrounding environment.

The atmospheric boundary layer (ABL) is the lowest part of the atmosphere that is continuously under the influence of the underlying surfaces through mechanical (roughness and shear) and thermal effects (cooling and warming), and the overlying, more free layers. Such boundary layers and the related geophysical turbulence exist also in oceans, seas, lakes and rivers. Here we focus on those in the atmosphere; however, similar reasoning as presented here also applies to the other geophysical flows mentioned. Since most of human activities and overall life take place in the ABL, it is easy to grasp the need for an ever better understanding of the ABL: its nature, state and future evolution. In order to provide a reasonable and reliable short- or medium-range weather forecast, a decent climate scenario, or an applied micrometeorological study (for e.g. agriculture, road construction, forestry, traffic), etc., the state of the ABL and its turbulence should be properly characterized and marched forward in time in concert with the other prognostic fields. This is one of many tasks of numerical weather prediction and climate models. Many of these models have problems in handling rapid surface cooling under weak or without synoptic forcing (e.g. calm nighttime mountainous or even hilly conditions).

Overall research during the last ∼ 10 years or so, strongly suggests that the evolution of the stable ABL is still poorly understood today. There we make a contribution by assessing some recent advances in the understanding of nature, theory and modeling of the stable ABL (SABL). In particular, we address inclined very (or strongly) stratified SABL in more details. We show that a relatively thin and very SABL, as recently modeled using an improved “z-less” mixing length scale, can be successfully treated nowadays; the result is quietly extended to other types of the SABL. Finally, a new generalized “z-less” mixing length-scale is proposed. At the same time, no major improvements in modeling weak-wind strongly-stable ABL is reported yet.

When modelling a flow in the atmosphere and the processes strongly influenced by it (e.g., the dispersion of air pollution), it is important to appreciate that the properties of both the flow itself and the dispersion are affected by the flow regime; i.e., whether the flow is turbulent (as is almost always the case in the atmosphere) or laminar. A second factor that might complicate atmospheric flow is stability, which depends on the nature of vertical temperature stratification.

In the first part of this chapter, we demonstrate the impact of vertical temperature stratification on flow structure, modelled via the Boussinesq approximation and by varying the Froude number (Fr). The flow is assumed to be laminar and is modelled in 2D.

Next, we review several approaches to treating turbulence in modelling studies, with an emphasis on an implicit large-eddy simulation. The results of Taylor—Green vortex computations performed using this method are compared with the results of a direct numerical simulation at moderate Reynolds numbers. Several quantities are considered, including the kinetic energy dissipation rate, probability density functions of turbulent fluctuations, and 3D energy spectra.

Turbulent flow over rough boundaries is a common occurrence in nature and the subject of much interest in a range of disciplines. It has long been recognized that the geometry of the boundary (or surface) dictates the flow and turbulence structure on a mean and instantaneous time scale. However, the mechanisms linking flow characteristics to roughness geometry remain poorly quantified, which has implications for our understanding of a variety of processes, particularly those occurring in the near-boundary region. It has been demonstrated that temporal and spatial variations in flow structure are sensitive to a range of geometric parameters describing the boundary geometry. We review the experimental evidence for rough boundary/flow interactions across different disciplines. A synthesis reveals that (1) different approaches have led to the adoption of a variety of parameters that are used to describe boundary roughness, and (2) that different criteria are used to evaluate the relative effects of boundary roughness. Moreover, (3) much of the experimental data relates to idealized surfaces that do not reflect the complexity of natural boundaries, or (4) is taken in low Reynolds number flows, and generally cannot be applied to aquatic flows in nature. The implications for our understanding of near-bed aquatic processes in turbulent boundary layers are discussed, and suggestions for future research approaches are presented.

Numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and appropriate bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme is used where central finite-differences, in the horizontal direction, and a pseudo-spectral approximation method with Chebyshev polynomials, in the vertical direction, are applied. A fractional time-step scheme is used for the temporal discretization. Over the rippled bed, the wave boundary layer thickness increases significantly, in comparison to the one over flat bed, due to flow separation at the ripple crests, which generates alternating circulation regions. The amplitude of the wall shear stress over the ripples increases with increasing ripple height or decreasing Reynolds number, while the corresponding friction force is insensitive to the ripple height change. The amplitude of the form drag forces due to dynamic and hydrostatic pressures increase with increasing ripple height but is insensitive to the Reynolds number change, therefore, the percentage of friction in the total drag force decreases with increasing ripple height or increasing Reynolds number.

The albedo of the interface has always been an important parameter for the evaluation of the radiation fluxes in environmental studies. The practical problem arises if the surface is a heterogeneous one. Various approaches to calculate the aggregated albedo have been developed. Our previous research demonstrated the existence of a geometrical effect when different parts of the interface have different heights. We have offered the general approach for the calculation of the flux that is lost due to the absorption on the vertical lateral boundaries. The multiple scattering effect and the dependence of the albedo on the zenithal angle of the incident radiation were disregarded. In the case of simple geometries we derived analytically the expressions for this loss coefficient, which, for some ideal urban geometries, coincides with Oke's sky-view factor. The aim of this chapter is an elaboration of this effect for more complex geometry, which does not allow analytic solutions. Therefore, it was necessary to develop an efficient numerical procedure, in this case the so-called ray-tracing Monte Carlo approach. It was first tested for known analytical solutions. As the next step, it was incorporated into one land surface scheme (LAPS), and then an example of central geometry was considered for: (i) a two-patch grid cell with a square geometrical distribution and (ii) different heights of its parts. Simulations were done for several patch areas, with different heights (“propagating building”). Various surface types were considered. The derived value for the albedo was compared with the result of the conventional approach. Changes in albedo lead to a significant change in partitioning of the energy at the environmental interface. The most remarkable changes were in values of sensible and latent heat fluxes, as well as the surface temperature. The values of effective surface temperature were calculated using the LAPS parameterisation scheme and then compared to the values obtained with a conventional parameterisation of the albedo.

Two methods for locating a possible source of air pollution that combine measurements and inverse modeling based on Bayesian statistics are proposed in this work. In both methods a puff model was used to generate the pollutant concentration field and the synthetic observations in predefined measuring points using real meteorological data. In the first approach the position of the possible source was found with an iterative process, defined as the maximum of probability density function from an ensemble of possible sources. The simplest form of the method was used, with a single source of known strength and known starting moment of the release. The simplicity of this approach and its numerical efficiency make it especially applicable for use in operational mode. Similar to the first method, the second method uses a library of records and scenarios, with combinations of values for the meteorological and emission parameters in the problem. This is done once, well in advance of the actual search for the source and can be computationally expensive. The second step is fully operational and is accomplished by calculating a marginal probability function from the observed concentrations of a pollutant at sampling points and those from appropriate scenarios.

Following a presentation of the brief history and present status of micrometeorological research activity in Hungary, the field measurement programs, instrumentation and flux calculation methodology are presented. The improvement in micrometeorological measurements and data acquisition system is also illustrated. Field experiments using the gradient and profile methods for trace gas fluxes were initiated in 1990. First, daily and annual variation in deposition velocities of ozone, nitrogen oxides and sulfur dioxide above grassland and spruce forest were investigated. The main goal of the investigations was the determination of the dry deposition velocity over different types of vegetation in different seasons. The measurements of dry deposition processes of nitrogen compounds, first of all of ammonia, over semi-natural grasslands, have been performed since year 2000. The ammonia fluxes are bidirectional, with net deposition on the annual time scale. Continuous measurements of the budget of energy, water, carbon and nitrogen, respectively, were carried out in the framework of EU5 (Greengrass) and EU6 (NitroEurope) projects in the central part of the country (“Bugac-puszta”) over grassland since 2002. One of the main objectives of this investigation is to reduce the large uncertainty in the estimation of CO₂, N₂O and CH₄ fluxes into and from plots of grassland under different climatic conditions. The final part of the paper illustrates the development of the new Hungarian basic climatological network for the detection of the possible effects of future climate change, which includes standard climate station measurements, soil profile (of temperature and moisture), radiation, energy budget components and CO₂ flux measurements. Based on continuous measurements of micrometeorological elements, trace gas concentrations and turbulent fluxes, more detailed information have been obtained of the structure and possible future changes of the surface layer and the intensity of the surface-biosphere-atmosphere interactions.

Fluid modeling covers a wide range of principles describing the motion of matter and energy in dependence on spatial scales, time scales and other attributes. In order to provide efficient numeric calculations, the information systems have to be developed for management, pre-processing, post-processing and visualization. In spite of that many software tools contain sophisticated subsystems for data management and implement advanced numerical algorithms, there is still need to standardize data inputs/outputs, wide used data analyses, and case oriented computational tools under one roof. Thus, the geographic information system (GIS) is used to satisfy all the requirements. As an example, the case study focused on dust dispersion above the surface coal mine documents the GIS ability to solve all the tasks. The input data are represented by terrain measurements of meteorological conditions and by estimates of the emission rates of potential surface dust sources. Remote sensing helps to identify and classify the coal mine surface in order to map erosion sites and other surface objects. GPS is used to improve the accuracy of the erosion site boundaries and to locate other point emission sources such as excavators, storage sites, and line emission sources such as conveyors and roads. The 3D mine surface for modeling of wind flows and dust dispersion is based on GPS measurements and laser scanning. All data inputs are integrated together with simulation outputs in the spatial database in the framework of the GIS project. In case of dispersion modeling, a few ways can be used to provide numeric calculations together with GIS analyses. The traditionally used way represents using of standalone simulation tools and the input/output data linkage through shared data files. The more advanced way is the implementation of dispersion models in the GIS environment. The methods are demonstrated by using U.S. EPA modeling tools and by linking standalone numerical calculations in the GIS environment with using case oriented programming libraries and GIS development tools.

Water distribution systems usually conduct good quality water, which is considered safe drinking water, to supply the population and thus satisfy its basic consumption needs. Water quality in the system depends on the quality level, which is normally controlled by the water treatment plant. Moreover, the possibility of elements surrounding the system entering the main itself (pathogen intrusion) can become an additional problem. This chapter describes the representation of pathogen intrusion in water distribution systems through experimental and numerical modeling in order to study one of the phenomena that cause drinking water contamination. Pathogen intrusion occurs when negative pressure conditions are achieved in the systems, allowing the entrance of water around a leak, causing a problem of water quality. The modeling process is based on experimental and computational procedures: an analysis of the behavior of intrusion considering hydrodynamic principles and transportation of pollutant is presented. In order to compare the results of the measurements and to visualize many other aspects, this case has been implemented in the CFD (Computational Fluid Dynamics) software FLUENT Inc. The computational model numerically solves the governing laws of Fluid Dynamics. These equations, taking into account turbulent phenomena, are solved in a geometric domain when a number of suitable boundary conditions are given. In CFD, the relevant magnitudes (velocity, pressure and concentration) are calculated in a discrete manner at the nodes of a certain mesh or grid and they are represented along the mesh. These computational models are especially useful when they have been validated, and we discuss the process for the calibration of both modeling techniques in this chapter. Through experimental and numerical models, we want to study steady state conditions of the leak and the subsequent mixture, entry and diffusion of the pollutant within the pipe to examine the phenomenon in detail and complement the experiences that will be developed in the laboratory. Computational Fluid Mechanics techniques become a powerful tool in this special problem to be used to obtain a deeper knowledge of the problem of pathogen intrusion into drinking water.

The presence of dead zones in streams and rivers significantly affects the characteristics of mass transport. In a river, dead zones can be due to geometrical irregularities in the riverbanks and riverbed and/or to spur dikes and groyne fields. Dead zones produce a difference between the concentration curves measured and modeled by the classical 1D advection-diffusion equation with sharper front and longer tails. In a dead zone, the mean flow velocity in the main stream direction is essentially zero and the main transport mechanism is transverse turbulent diffusion which controls the exchange processes of solutes with the main stream. This Chapter presents the results of 3D steady-state and time-variable numerical simulations carried out with Multiphysics 3.5™ in a rectangular channel with a lateral square cavity representing a dead zone. This geometry was previously experimentally studied by Muto et al. [18] [19]. The exchange coefficient between the main flow and the dead zones was calculated both from the transverse velocity data along the dead zone-main channel interface and from the temporal decay of the concentration of a tracer that was homogeneously injected in the dead zone.

Mercury in the aquatic environment is a neurotoxin with several known adverse effects on the natural ecosystem and the human health. Mathematical modeling is a cost-effective way for assessing the risk associated with mercury to aquatic organisms and for developing management plans for the reduction of mercury exposure in such systems. However, the analysis of mercury fate and transport in the aquatic environment requires multiple disciplines of science ranging from sediment transport and hydraulics, to geochemistry and microbiology. Also, it involves the knowledge of some less understood processes such as the microbial and diagenetic processes affecting the chemical speciation of mercury and various mechanisms involved in the mass-exchange of mercury species between the benthic sediments and the overlying water. Due to these complexities, there are many challenges involved in developing an integrated mercury fate and transport model in aquatic systems. This paper identifies the various processes that are potentially important in mercury fate and transport as well as the knowns and unknowns about these processes. Also, an integrated multi-component reactive transport modeling approach is suggested to capture several of those processes. This integrated modeling framework includes the coupled advective-dispersive transport of mercury species in the water body, both in dissolved phase and as associated to mobile suspended sediments. The flux of mercury in the benthic sediments as a result of diffusive mass exchange, bio-dispersion, and hyporheic flow, and the flow generated due to consolidation of newly deposited sediments is also addressed. The model considers in addition the deposition and resuspension of sediments and their effect on the mass exchange of mercury species between the top water and the benthic sediments. As for the biogeochemical processes, the effect of redox stratification and activities of sulfate and iron-reducing bacteria on the methylation of mercury is discussed, and the modeling approach is described. Some results for the application of the model to the Colusa Basin Drain in California are presented. At the end of the paper, the shortcomings of our current knowledge in predicting the fate of mercury in water-sediment systems, the potential improvements, and additional complexities required to make the model more realistic, are discussed.

The present work is aimed to study the distribution of the temperature and the phytoplankton biomass in the near-shore Aveiro coastal zone (Portugal) using a threedimensional ecological model. The study area is located in the western coast of the Iberian Peninsula, characterized by meteorological conditions of strong north/northwest prevailing winds, which favours the upwelling of nutrient enriched waters resulting from the divergences associated to the Ekman transport and, therefore, generating high nutrients availability. The results show that the model is able to reproduce the horizontal and the vertical temperatures and chlorophyll-a (Chl-a) patterns. They show, as well, the setup of a layer of cold water along the coastal side and the increasing of the declivity of the thermocline and the nutricline toward the coast. The model predicts satisfactorily the values for the maximum Chl-a concentration and the depth of the inshore subsurface chlorophyll maximum. The chlorophyll-a concentration shows maximum concentration values higher than 6 mg m⁻³, during summer, near the coast. The subsurface chlorophyll-a maximum concentration is located within the euphotic zone, about 10 m bellow the surface, near the coast, deepening to value close to 40 m offshore.

This chapter deals with the calibration of a new simplified experimental method to evaluate absolute roughness of vegetated channels. The method is based on boundary layer measurements in a short channel rather than on uniform flow measurements, as usual. The proposed method can be applied to any kind of rough bed, but it is particularly useful in vegetated beds where long channels are difficult to prepare. In this paper a calibration coefficient is experimentally obtained. In order to perform suitable comparisons with literature data relationships between ε absolute roughness and Manning's n coefficient are deepened. The results are successfully compared with literature experimental data with a very good fit. Finally, a particular dependence of ε values on the vegetation density are explained through further experiences. In conclusion it is possible to state that the proposed method, once calibrated, can provide reliable prediction of absolute roughness in vegetated channels.

The following sections are included:

• Index