The main objective of this research project is to quantify Lagrangian and Eulerian statistics from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. In particular, the fields of the Eulerian and Lagrangian time scales of the turbulence will be investigated together with their dependence on the aspect ratio of the canopy AR, i.e. the ratio of the width to the height of the canyon. The latter must be considered as an archetype for more complex geometrical situations generally found in real cities. The Lagrangian time scale (TL) is a key parameter for pollutant dispersion modelers; however, its experimental determination is still a difficult task, particularly in the case of inhomogeneous, turbulent flows. For this reason, that issue has not been much addressed in the past and there is still a lack of knowledge on TL because of measurements difficulties. Therefore, we aim to determine its spatial distribution as well as to establish its possible functional dependence on the AR.
Lagrangian velocity measurements will be performed using a feature tracking technique that recognizes particle trajectories by means of a dedicated algorithm. With this technique individual particle trajectories are illuminated throughout a volume of the flow and tracked using a camera. Though particle tracking has previously been used in the past to obtain experimentally Lagrangian statistics, measurements permitting the direct estimation of Lagrangian time scales of turbulence pertaining to canopy flows have not been reported in the literature.
In addition, Eulerian quantities such as mean velocity, velocity variance, momentum flux, dissipation rate of turbulent kinetic energy and the Eulerian time scale will be also determined for each of the AR considered in the study. Information on other parameters of the turbulence of interest in dispersion studies such as the eddy diffusivity of momentum and the Kolmogorov constant will also be given.
The importance of the Lagrangian time scale of turbulence stems from the fact that it is one of the main parameters involved in Lagrangian models of turbulent dispersion. These can be easily coupled with common Reynolds-averaged Navier-Stokes models (RANS), which have gained a growing interest owing to their relatively small computational cost. RANS models, however, do not compute the Lagrangian time scale that must be estimated from parametric laws founded on theoretical bases and generally applicable only to simple cases (e.g. flat terrain).
Theoretical predictions of the Lagrangian time scale valid on complex terrain are not known. On the other hand, its experimental determination is not simple, especially where the geometry leads to a strong spatial variability of the flow. As far as we are aware, direct estimation of Lagrangian time scales pertaining to canopy flows have not previously been reported in the literature.
Another salient aspect of this research regards the estimation of other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum and the Kolmogorov constant, C. The latter comes from Kolmogorov's theory of local isotropy (Monin and Yaglom 1975) and is involved in the expression of the random forcing of LSMs. Numerous experimental and numerical studies have been performed with the aim of determining C. Nevertheless, there is still no consensus among the scientific community about its value, and C is generally assumed to fall within the range 2-7 (see Poggi et al. 2008 for a review on C values found in the literature). Even more important, the present experimental apparatus permits to assess possible anisotropies of C, that is, whether or not Cx=2*Sx^2/(TLx*E) differs from Cz=2*Sz^2/(TLz*E). Here, TLx and TLz represents the Lagrangian time scale calculated for the streamwise and the vertical velocity component, respectively.
Furthermore, it is of interest to compare Cz with those obtainable using two further estimations of Cz, both valid for the equilibrium range and currently used in LSMs. The first one is derived by matching the Taylor and the Prandtl expressions of the turbulent diffusivities, viz.: Cz=2*(Sz/u*)^4. The second form for Cz comes from TLz=0.4*z/u*, viz.: Cz=2*(Sz/u*)^2, where Sx and Sz are the standard deviations of the streamwise and the vertical velocity components, respectively.
Finally, the experimental apparatus available for this research project has proven to be effective in previous studies regarding urban canopy flows performed in recent years by the present research group. The use of the image analysis is certainly a useful tool to perform velocity measurements with high spatial and temporal resolution, which is a necessary condition to obtain reliable measurements of the Lagrangian time scale of the turbulence.