density gradient. Emphasis is placed on the first application and 

 detailed comparison with data. In the second example, a canopy model 

 with some preliminary application is presented. In the third example, 

 adaptation of a condensed version of the turbulent transport model to a 

 mesoscale hydrodynamic model of coastal, estuarine, and lake currents 

 will be outlined. 



A TURBULENT TRANSPORT MODEL 



The model equations of motion for an incompressible fluid in the 

 presence of both a gravitational and a Coriolis body force, witn the 

 mean variables denoted by capitals and the turbulent fluctuations by 

 lower-case, may be written in general tensor notation as follows: 



dU 



au< 



1 °"i 



at J axj 



^"i"j _ 1 ap 

 axj p axj^ 



(G-Gq) 



-2eiji,QjUj, + 



ax. 



aui 

 ax. 



(1) 



au^ 

 axi 



(2) 



ae ,, aQ 

 at J axi 



^"j! . _a_ /^ ae. 



axj axj^ I axj^ 



(3) 



au^Uj au^Uj 



at 



+ u. 



ax. 



au. 



aUi u.e u^e 



= -u^u,, — '^ -u.,u„ +g. -=^ +g^ — -2zii,t,Qy. u„u 



^ ** ax^ J '^ ax^ ^ Go J Go ii^A i< i J 



au.u 



i"j 



- 2ejju, Q, u^Ui * 0.3 — l^qA j- ^ ^-^-j - .,, 3 .- .,, ^^^ 



- r \UiUi - 6i s ^ - 6 



(4) 



au.e 



au. e 



i" „ "-i' 



Uj = - U.U; 



ae —= s"i 

 at ^ axj ^ J axj J axj 



^"i® \ 0.75q 



+ 8i 



* °-3 ^ r =«j 



u.e 



- 2eiji, Qj Uj^( 



(5) 



ae^ „ ae^ ^ — r ae „ , a / . a9^\ o.^sge^ 



— ♦ u^ — = - 2 u.e — + 0.3 — |qA — I 



at J axj J axj ax. V axj / a 



(6) 



aA 



aA 



au. 



■^ + U. -i^^ = 0.35 ^ u.u. — - + 0.6bq + 0.3 -^ |qA 



at J ax. q2 ^ J axi 



axi 



aA 

 axi 



236 



