Theory of Turbulent Flow Between Parallel Plates 



where time-averaged quantities are under a bar, vectors are in black type, and 



For the fluctuating state; 



^Ri + Ro -DR^,) + R^i^ -DRo = -□?(!) + n'Rd) + qn(n -Rd)) 



T~ ^( 1 ) + Rq ' ^'^(1) + R( 1 ) • n 3'c 



- O'oo- 1) 



Br 



■P(i) + Ro -nPd) + R(,) -nPoJ = ^.^ [Roi. ^ + Roj ,1^ R(i)j,i 



(5) 



(^^(1) + «o-n3'(i) + R(i) -D^o) 



-^o ^P(i) + «o -nPd) + R(i) -nPo 



= R 



( 1) j . j 



BOUNDARY CONDITIONS 



The following boundary conditions are assumed for one -dimensional long- 

 channel flow between parallel plates. For the fluctuating field components, let 



R 



( 1) 



(iU(i) + JVd) + kW(j^) = v(iu+jv+kW) eJ^-^^°'>'^^^) 



represent the components of the fluctuating flow; 



R^j^ = at X = ±1 (velocity zero at the walls), 



J^i) = at X = ±1 (temperature deviations zero at the walls). 



For the mean field components, let 



Rq = kRo(x) =kR„Jl-<p(x)] 



represent the undetermined form of the mean velocity; 

 Rq (x) = at X = ±1, 



Po(0 = -gz. 

 g is assumed to be constant independent of x ; 



Jo(x) = ■. 



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