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Classical fluid mechanics developed during the XVIIIth and XIXth centuries and the first half of the XXth century dealt mainly with flows over smooth or rough surfaces. The idealization of a sand roughness suggested by L. Prandtl and I. Nickuradze was quite sufficient and successful for contemporaneous problems and brought light to many engineering inventions, as well as for the applications of fluid mechanics in hydraulics and meteorology of that time. No real attention was paid to the fluid motion between roughness elements.

As with other characteristic types of complex fluid flows, turbulent flows over and between different types or flexible obstacles above resistive surfaces have many features in common. This is why such flows can be studied in a similar conceptual framework and with similar techniques of analysis, computation and measurement.

In this chapter, several simple flow models will be considered for different structures of the easily penetrable roughness. Generally, two EPR structures will be investigated. In Section 3.1, it will be taken for simplicity that the EPR consists of small spheres ‘trapped’ in the volume. Therefore, no equations will be required for characterizing the ‘medium of obstruction’. This structure is called the “EPR made up of immobile elements”. In contrast, the obstructions in Section 3.2 will be allowed to move along the wind (“EPR made up of mobile elements”, or “Droplet EPR”). Analytical solutions will be derived whenever it is possible.

Terrestrial vegetation canopies are obvious examples from the natural world of flow and transport in complex obstructed geometries. Observations of turbulence structure in vegetation canopies date back almost forty years (Wright and Lemon, [654]; McBean, [402]; Allen, [6]; Baines, [19]; Isobe, [307]; Shaw et al., [571]). One of the earliest observational studies of the budget of turbulent kinetic energy inside a forest is that of Lesnik [369]. This latter author appears to have been the first to illustrate the importance of the diffusion of turbulent kinetic energy between levels in the canopy, and to point to the significance of the large difference in scale of turbulence between that created by large-scale shear near the canopy top and that resulting from wakes behind individual canopy elements. It is now clearly apparent that turbulence over and within plant canopies differs significantly from that over smoother surfaces. In particular, velocity spectra are more sharply peaked, streamwise and vertical velocities are strongly (negatively) correlated and are each highly skewed, and transport is dominated by organized structures with ejections from the canopy preceding downward sweeps of high momentum fluid. Excellent reviews of flow and turbulence in plant canopies can be found in Raupach and Thom [522] and, more recently, in Finnigan [187].

Over the last twenty five years a consistent picture of the structure and dynamics of canopy turbulence has emerged. We now know that there are fundamental differences between the structure of turbulent flow through uniform vegetation canopies and that in a boundary layer. The flow in and above the canopy, that is, in the ‘roughness sublayer’ resembles that in a plane mixing layer rather than a boundary layer. Turbulence production rates near the canopy top are much higher than in a boundary layer and characteristic large, energy-containing eddies, quite distinct from those in the boundary layer above are generated there by a hydrodynamic instability process. In the canopy, the dissipation rate of turbulence is also enhanced because boundary layers on the vegetation surfaces provide a source of intense shear layers with thicknesses of order the Kolmogorov lengthscale, augmenting those in the normal eddy cascade. This paper describes the way that this ‘standard’ picture of canopy turbulence is modified by topography so it is appropriate to set the scene with a brief history of how this standard picture was constructed. As scientific histories generally are, this will be a personal account, reflecting the line of discovery followed over the last three deacdes by the group

As a bridge to Chapter 4 in this book, it is useful to begin with a comparison of terrestrial and aquatic systems. The range of flow condition observed in aquatic systems is depicted in Figure 6.1. Conditions span from the unconfined canopy, in which the flow depth is much greater than the canopy height, to the emergent canopy, in which the canopy fills the entire flow depth. Consider Figure 6.1a, which depicts an unconfined canopy that closely resembles terrestrial conditions (see also Figure 4.1a). The discontinuity in drag at the top of the canopy creates a region of strong shear. This region of the velocity profile resembles a free-shear-layer and includes an inflection point just within the canopy. A free-shear-layer is characterized by large coherent vortices that form via Kelvin-Helmholtz (K-H) instability and which dominate the transport across the layer [86, 649]. In terrestrial canopies, these coherent structures have been shown to play an important role in transport between the canopy and overlying atmosphere [187, 194, 530]. Far above the canopy the flow returns to a boundary layer structure. The in-canopy flow is driven by the turbulent stress at the top of the canopy, and it decays with distance from the top of the canopy due to the significant momentum

Many environmental and processing engineering flows consist of collections of fixed or moving bodies (such as buildings, plants, bubbles and droplets). These flows may be unbounded or bounded high Reynolds number flows through groups of bodies, such as crop ‘canopies’ or buildings in the atmospheric boundary layer, boiler tubes in a furnace, flows through moving objects such as icebergs in the ocean, or bubble swarms in pipes. Examples of buildings in the urban terrain are given in Chapters 2 and 8, while plant canopies are described in Chapters 4 and 6. For many problems, the goal is to model the impact of many bodies on the ambient flow. There is an intrinsic complexity to modelling the flow through and around a group of bodies and estimating the flow signature they generate. In many cases, the huge number of bodies and the range of geometrical lengthscales (eg. from leaf size, to tree size, up to a forest scale, for plant canopies) means that traditional computational models, where the whole flow domain is meshed and solved numerically, are not able to include all the geometrical aspects [596]. As such, average descriptors, such as a distributed drag force introduced into

Uncontrolled fires and their associated smoke have been part of mankind’s hazard environment since prehistoric times. Fires caused by lightening or volcanic activity moved across the earliest vegetative landscape whether grassland or forest scourging away all life before its path. Later, as man collected into groups and tribes, villages, towns and cities were routinely wiped away as natural, accidental, war or arson sources provided ignition. Most cities were not burned to the ground once, but multiple times. Even today massive wild fires in forests occur every year all over the world, and the threat of mass fires in cities haunt the minds of those concerned by large petrochemical accidents, wars or terrorism.

The quality of the urban air pollution forecast and the Urban Air Quality Information and Forecasting Systems (UAQIFS) critically depends on the: (i) mapping of emissions, (ii) level of urban air pollution (UAP) models, and (iii) quality of meteorological fields in urban areas. The main problem in forecasting of UAP is the prediction of episodes with high pollutant concentration in urban areas. In these areas most of the well-known methods and models, based on in-situ meteorological measurements, fail to produce realistically the meteorological input fields for the UAP models. Many projects are aimed at developing UAP dispersion models and chemical transformation efforts were put to improving forecasts of meteorological parameters in UAP models. These would be especially important in air pollution episodes (APEs) with low winds, stable stratification, local air circulations, topographic effects, breeze conditions, and internal boundary layers. Moreover, a reliable urban scale forecast of air flows and meteorological fields is of primary support for urban emergency management systems for and at improving knowledge about pollutants and emissions. However, no significant