Theory of Turbulent Flow Between Parallel Plates 

 SUGGESTIONS FOR FURTHER DEVELOPMENT 



In this paper the problem is not completed. Instead, this section offers 

 some ideas for further development. 



Solutions Near The Wall 



Returning now to the solutions within the boundary layer, we can evaluate 

 the constants of integration to obtain the following primitives that satisfy wall 

 boundary conditions. 



X = +1 



U = + mil [(l-a) S - 2ea^2gaj ^32^2 a 

 7-1 p-^^3'' 



.+ (Sg/2<:^)x p-^2' 



• ^/2^-^ e 2 



v^ 



1 + 



y - 1 



V = a [(1-cr) 5 - 2ecr/32gaj] A 



± j ajX 



jaj 



X = -(1-cr) /32aj2A 



L e 

 ± j a jX ± ( Sg/2co)x Icjx 



ja. 



IjaoX +C.X 



3'=-(7-l)a;A[(l-cr)S- 2eCT/32gaj 

 P = oj [(l-cT) S - 2ea/S2gaJ A 



ja 



where 



4 = (1- j) ^y , C^ = (1+ J) ^^ , 83 = CI- J)y 2 



(1-J) 



yf2^ 



1 + 



7 - 1 



a2 + 82 = /32^2 _ 



-/32g v^ 



/32aj2 



,,21:^^ * ,*c,.i^ 



1 + 



- 1 



g \ 2co 



While h is restricted to its nonpositive domain, there are the conjugate 

 sets e*J(-°y^^^*'"^). 



What we have derived is a primitive system of self- generated traveling 

 wavelets in the boundary layer that act as a source of "acoustically" derived 



729 



