Our model also computes the dynamic length scale of turbulence, A, 

 which is a representation of the mean turbulent eddy size. The ratio 

 between this length scale and the total velocity variance, q, 

 represents the time scale associated with the eddy motion. In 

 sediment-laden flows, the relaxation time of sediment particles (irf-/g. 



where W =settling speed) relative to the time scale of turbulent eddies 



lii< 

 determines whether the particles follow the turbulent eddy motions or 

 not. For a given particle size, there exists a height below which the 

 sediment particles do not follow the turbulent eddy motions and hence 

 the interaction between the particles and the turbulent eddies has to 

 be considered. In such case, the use of a dynamic turbulence model, as 

 opposed to an eddy-viscosity model, is highly desirable and 

 recommended. Tooby et al . (9) performed an interesting laboratory 

 study on the "vortex trapping mechanism" in affecting the suspended 

 sediment concentration in an oscillatory turbulent boundary layer. To 

 include such a mechanism in a predictive model for sediment 

 concentration, it is essential to consider the interaction between 

 sediment particles and turbulent eddies by means of a turbulent 

 transport model such as ours. 



TRANSPORT OF MOMENTUM, HEAT, AND MASS WITHIN A VEGETATION CANOPY 



A canopy of vegetation represents a complex lower boundary for 

 hydraulic and atmospheric flows (Figure 6). For flow well above this 

 canopy, it is usually adequate to characterize the boundary in terms of 

 only an aerodynamic roughness, Z^. But when one is interested in the 

 flow within the canopy or immediately above it, a more detailed 

 representation is required. 



Flow in vegetated waterways has been modeled empirically (e.g., ^, 

 10) . Although such empirical models may be useful for qualitative flow 

 analysis, a more complete model is required for quantitative estimation 

 of the transfer of momentum, heat, and species within the vegetated 

 environment. Second-order closure models for canopy flow have recently 

 been developed by Wilson and Shaw (20), and Lewellen and Sneng (13). 

 The principal difference between these two models is that the latter 

 consider heat and species transport as well as momentum transport. 

 Lewellen and Sheng also used a more general representation of the drag 

 per unit volume of the vegetation. The model can predict the variation 

 in surface layer heat and species transport as a function of surface 

 Reynolds number, Prandtl number, Schmidt number, and plant area density 

 distribution. Although the basic canopy model was originally designed 

 to aid in the prediction of the dry deposition of gaseous SO2 and 

 particulate sulfate in the atmosphere, it is quite general and nence 

 provides a basic framework for extension to hydraulic applications. 



The canopy introduces source and sink terms into the basic 

 conservation equations. The total drag force due to the canopy is 

 composed of a skin friction drag and a profile drag. The skin friction 

 drag forces of the canopy can be estimated by multiplying the shear 

 stress across the laminar sublayer near the leaf surfaces by the total 

 leaf surface area per unit volume. In addition to the skin friction 

 drag, however, a more important pressure drag is generally imposed by 

 the pressure difference between the upwind and downwind surfaces of a 

 leaf or other obi ^(Lfc_i.o_the- flow. We take-the-tatal—<l<^g— term— due— ttr- 



241 



