It has often been remarked that turbulence is a subject of great scientific and technological importance, and yet one of the least understood (e.g. McComb 1990). To an outsider this may seem strange, since the basic physical laws of fluid mechanics are well established, an excellent mathematical model is available in the Navier-Stokes equations, and the results of well over a century of increasingly sophisticated experiments are at our disposal. One major difficulty, of course, is that the governing equations are nonlinear and little is known about their solutions at high Reynolds number, even in simple geometries. Even mathematical questions as basic as existence and uniqueness are unsettled in three spatial dimensions (cf Temam 1988). A second problem, more important from the physical viewpoint, is that experiments and the available mathematical evidence all indicate that turbulence involves the interaction of many degrees of freedom over broad ranges of spatial and temporal scales. One of the problems of turbulence is to derive this complex picture from the simple laws of mass and momentum balance enshrined in the NavierStokes equations. It was to this that Ruelle & Takens (1971) contributed with their suggestion that turbulence might be a manifestation in physical

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The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows

The science of the total environment

The complexity of flow and wide variety of depositional processes operating in subaqueous density flows, combined with post-depositional consolidation and soft-sediment deformation, often make it difficult to interpret the characteristics of the original flow from the sedimentary record. This has led to considerable confusion of nomenclature in the literature. This paper attempts to clarify this situation by presenting a simple classification of sedimentary density flows, based on physical flow properties and grain-support mechanisms, and briefly discusses the likely characteristics of the deposited sediments. Cohesive flows are commonly referred to as debris flows and mud flows and defined on the basis of sediment characteristics. The boundary between cohesive and non-cohesive density flows (frictional flows) is poorly constrained, but dimensionless numbers may be of use to define flow thresholds. Frictional flows include a continuous series from sediment slides to turbidity currents. Subdivision of these flows is made on the basis of the dominant particle-support mechanisms, which include matrix strength (in cohesive flows), buoyancy, pore pressure, grain-to-grain interaction (causing dispersive pressure), Reynolds stresses (turbulence) and bed support (particles moved on the stationary bed). The dominant particle-support mechanism depends upon flow conditions, particle concentration, grain-size distribution and particle type. In hyperconcentrated density flows, very high sediment concentrations (>25 volume%) make particle interactions of major importance. The difference between hyperconcentrated density flows and cohesive flows is that the former are friction dominated. With decreasing sediment concentration, vertical particle sorting can result from differential settling, and flows in which this can occur are termed concentrated density flows. The boundary between hyperconcentrated and concentrated density flows is defined by a change in particle behaviour, such that denser or larger grains are no longer fully supported by grain interaction, thus allowing coarse-grain tail (or dense-grain tail) normal grading. The concentration at which this change occurs depends on particle size, sorting, composition and relative density, so that a single threshold concentration cannot be defined. Concentrated density flows may be highly erosive and subsequently deposit complete or incomplete Lowe and Bouma sequences. Conversely, hydroplaning at the base of debris flows, and possibly also in some hyperconcentrated flows, may reduce the fluid drag, thus allowing high flow velocities while preventing large-scale erosion. Flows with concentrations <9% by volume are true turbidity flows (sensuBagnold, 1962), in which fluid turbulence is the main particle-support mechanism. Turbidity flows and concentrated density flows can be subdivided on the basis of flow duration into instantaneous surges, longer duration surge-like flows and quasi-steady currents. Flow duration is shown to control the nature of the resulting deposits. Surge-like turbidity currents tend to produce classical Bouma sequences, whose nature at any one site depends on factors such as flow size, sediment type and proximity to source. In contrast, quasi-steady turbidity currents, generated by hyperpycnal river effluent, can deposit coarsening-up units capped by fining-up units (because of waxing and waning conditions respectively) and may also include thick units of uniform character (resulting from prolonged periods of near-steady conditions). Any flow type may progressively change character along the transport path, with transformation primarily resulting from reductions in sediment concentration through progressive entrainment of surrounding fluid and/or sediment deposition. The rate of fluid entrainment, and consequently flow transformation, is dependent on factors including slope gradient, lateral confinement, bed roughness, flow thickness and water depth. Flows with high and low sediment concentrations may co-exist in one transport event because of downflow transformations, flow stratification or shear layer development of the mixing interface with the overlying water (mixing cloud formation). Deposits of an individual flow event at one site may therefore form from a succession of different flow types, and this introduces considerable complexity into classifying the flow event or component flow types from the deposits.

The physical character of subaqueous sedimentary density flows and their deposits

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

This paper reviews methods to evaluate the performance of air quality models, which are tools that predict the fate of gases and aerosols upon their release into the atmosphere. Because of the large economic, public health, and environmental impacts often associated with the use of air quality model results, it is important that these models be properly evaluated. A comprehensive model evaluation methodology makes use of scientific assessments of the model technical algorithms, statistical evaluations using field or laboratory data, and operational assessments by users in real-world applications. The focus of the current paper is on the statistical evaluation component. It is important that a statistical model evaluation exercise should start with clear definitions of the evaluation objectives and specification of hypotheses to be tested. A review is given of a set of model evaluation methodologies, including the BOOT and the ASTM evaluation software, Taylor’s nomogram, the figure of merit in space, and the CDF approach. Because there is not a single best performance measure or best evaluation methodology, it is recommended that a suite of different performance measures be applied. Suggestions are given concerning the magnitudes of the performance measures expected of “good” models. For example, a good model should have a relative mean bias less than about 30% and a relative scatter less than about a factor of two. In order to demonstrate some of the air quality model evaluation methodologies, two simple baseline urban dispersion models are evaluated using the Salt Lake City Urban 2000 field data. The importance of assumptions concerning details such as minimum concentration and pairing of data are shown. Typical plots and tables are presented, including determinations of whether the difference in the relative mean bias between the two models is statistically significant at the 95% confidence level.

Air quality model performance evaluation

Transport of a passive scalar contaminant in nearly isotropic non-decaying turbulence was first studied theoretically by Corrsinl, and in that study it was predicted that an imposed passive linear cross-stream mean temperature profile will maintain itself and will be independent of the downstream distance. Corrsin’s prediction of constancy of the cross-stream temperature gradient, s, has been confirmed experimentally for decaying turbulent flows2,3,4. Despite the constancy of s there has been confusing experimental data on the streamwise evolution of passive scalar contaminants. The heated grid method used by Wiskind2 to study the streamwise evolution of passive scalar has been found to be far from ideal because significant transverse variation of temperature variance was observed in Wiskind’s data3,4. The use of differentially heated screens downstream of a grid3,4 has aided the study of the streamwise evolution of passive scalar fluctuations, but there still remains some uncertainties in the physics of this type of flow particularly at large decay times.

Molecular and Stratification Effects on the Evolution of Concentration Fluctuations in Decaying Homogeneous Turbulence with Transverse Mean-Concentration Gradient

In recent years there has been an increasing availability of high-resolution 3-D urban databases, which can be used for the analysis and measure of city geometry (urban morphometry). In the context of urban morphometry, Ratti et al. (2001) described a method to extract various parameters from urban Digital Elevation Models (DEMs) by using imageprocessing techniques. As DEMs are becoming increasingly common some questions arise on how best to use them in the modelling of urban wind field and dispersion. In this paper we discuss some applications of DEMs to: (1) the calculation of the aerodynamic roughness length 0 z for the city as a whole and its spatial variation ) , ( 0 y x z on the neighbourhood scale; (2) the estimation of the flow over the city from ) , ( 0 y x z and using both linearised perturbation modelling and computational fluid dynamics (CFD); (3) the modelling of mean wind profile within and above the urban canopy.

Modelling the urban flow field and pollution dispersion using digital elevation models

This work presents selected results of an EPSRC-funded project investigating the dispersion of nanoparticles in the wake of moving vehicles. The aims were to study the changes in particle number distribution (PND) due to the competing effects of dilution and transformation processes (e.g. coagulation, nucleation, condensation) over the travel time from tailpipe to roadside, and to model the fate of these particles in the near and the far wake regions of a moving vehicle. To achieve these objectives, firstly ground-fixed and on-board measurements of PNDs were performed using a fast response (sampling frequency up to 10Hz) differential mobility spectrometer (Cambustion DMS50) in the wake of a diesel engined car moving at a range of speeds from 20 to 50 km h -1 . Secondly, wind tunnel simulations were carried out on reduced scale (1:5 and 1:20) models of the car used for the field experiments. The flow and turbulence fields were characterised both in the near and far wake of the modelled vehicle by using a two component laser Doppler anemometer. Concentration measurements were obtained by using a fast response (frequency >350 Hz) flame ionisation detector and a hydrocarbon tracer gas released from the modelled tailpipe. A high resolution experimental data base was obtained from both the field and wind tunnel measurements for formulating the basis of fast mathematical parameterisations that can be used with operational nanoparticle dispersion models.

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Understanding dispersion of nanoparticles in vehicle wakes combining field measurements and wind tunnel simulations

Air quality around airports

Within the scope of the European ATREUS network were developed methodologies aiming at the optimization of the energy consumption of buildings in relation to their cooling and heating requirements These are strongly related to the micro-climatic conditions that develop within the vicinity of buildings and particularly the wind speed, temperature and humidity On the large scale we used the ECMWF ERA-40 archive and the meso-scale model MM5 to provide solutions without detailed analysis of the near-surface region We then used two methodologies in order to produce detailed micro-meteorological profiles within a real urban canopy The first method is based on the exchange of momentum and mass between the urban canopy and the urban boundary layer above, by using spatially-averaged wind profiles over the canopy volume The second is based on Computational Fluid Dynamics (CFD) simulations, which provide high-resolution details on the spatial distribution of the wind and temperature

Rex Britter

Papers

Molecular and Stratification Effects on the Evolution of Concentration Fluctuations in Decaying Homogeneous Turbulence with Transverse Mean-Concentration Gradient

Modelling the urban flow field and pollution dispersion using digital elevation models

Understanding dispersion of nanoparticles in vehicle wakes combining field measurements and wind tunnel simulations

Air quality around airports

From meso-scale to street-scale: a downscaling procedure using statistical and CFD models.The Lisbon case study