Mean velocity profile, turbulence parameters

We conclude that over the continuum scale the determining parameters are the wind speed Uh and turbulence initial parameters of the cloud/plume when it reaches the top of the canopy or, equivalently, the virtual source at the level of the canopy. Using suitable fast approximate models for the flow field over urban areas (e.g. RIMPUFF, FLOWSTAR), the variation of the mean velocity and turbulence above the canopy can be calculated. The FLOWSTAR code (Carruthers et al., 1988 [105]) has been extended to predict how (Uc) varies within the canopy. Dispersion downwind of the canopy can also be estimated using cloud/plume profiles, denoted by Gc,w,GA,w which are shown in Figures 2.20 and 2.22. 

The Reynolds stress distributions in Fig. 8.5c indicate that turbulent momentum transport is also modified at high levels of counterflow. Since the mean velocity profiles (shown in Fig. 8.4) display independence of i, but the Reynolds stress experiences enhanced transport, the overall turbulent production of the layer is considerably increased above 13%) counterflow. In fact, a comparison of the self-similar stress profiles in Fig. 8.5 indicates that a common state is achieved for < 0.13(/i, and a second common self-similar state is achieved for U2 > 0.24(7i. From 0% to 13% counterflow, the turbulent profiles collapse, indicating a mechanism for generating the turbulence that scales with the growth rate parameter o- and velocity difference AU. Above 13% counterflow, there is an increase in turbulence level across the entire cross-stream extent of the layer. This increase seems to be dependent on velocity ratio, but not on the parameter c. Since the mean profiles display similar shape, there is likely an additional mechanism for turbulence production when Ibol is greater than approximately 0.13f7i. 

The shear stresses over the flow boundaries can be rigorously derived as an integral part of the solution of the flow field only in laminar flows. The need for closure laws arise already in single-phase, steady turbulent flows. The closure problem is resolved by resorting to semi-empirical models, which relate the characteristics of the turbulent flow field to the local mean velocity profile. These models are confronted with experiments, and the model parameters are determined from best fit procedure. For instance, the parameters of the well-known Blasius relations for the wall shear stresses in turbulent flows through conduits are obtained from correlating experimental data of pressure drop. Once established, these closure laws permit formal solution to the problem to be found without any additional information. 

---