the canopy as 



V<='f 



Vf (UUj/q ) 



21/2 



q U^: with Cf=cJ — 



(8) 



where c^. is the skin friction drag coefficient and c^ is the profile 

 drag coefficient. The frontal area per unit volume, A^., and the wetted 

 area per unit volume, A , appear in Equation (8). These two areas 

 differ at least by a factor of two and in moderate flow conditions when 

 the leaf aligns itself with the flow they can differ by an order of 

 magnitude. 



The sink terms in the energy and species equations may be obtained 

 similarly by considering the transfer of heat and species across the 

 sublayer as 



^r-"^ A a (e-0j 



(9) 



C = Ci 



£ )0.7 



V 



1 ♦ Cr( - 



0-7 



q R. 



VC = Cc^w'^C 



(10) 



In summary, a term -Dj, is added to the mean momentum equation (1), 

 a term -Q is added to the mean energy equation m) , and the mean 

 species equation can be written as 



5C „ ac . ^ dCUjC-rfgC) 

 — + U^ = -c. A^qC 



at J axj c w^ ax^ 



ax. 



ac 

 ax. 



(11) 



Both a source and a sink term need to be added to the Reynolds stress 

 equations: 



au^u. 2 



1/2 



q ) '^^ Af Uj^u. 6^. -2c^ A^q u^u. (no sum i,j) + . 



(12) 



The first term represents the creation of wake turbulence due to 

 the profile drag, while the second term recognizes that the skin 

 friction can also dissipate the turbulent fluctuation of velocity. The 

 profile drag can also break up the eddies to increase the dissipation, 

 but this is accounted for in the model by introducing an additional 

 constraint for A which is inversely proportional to the plant area 



density, i.e., A < a/(c A). Additional sink ter ms are ^added to the 



temperature and species correlation equations for u^Q, u^c , 9^, c^, and 

 ce. 



The computational domain extends from z=0 at the bottom to z=2h, 

 twice the canopy height. At the top boundary, the mean variables are 



242 



