Theory of Turbulent Flow Between Parallel Plates 



Wall Solutions 

 Mode I 



± j a, X 



2 = -\ - 



JO) ; a, 



2co 



j 1 + ^ 



X = 1 



U = , 



V = -aw[(l-a-) S - 2ea-/32gaj] Aj e ^ , 



X = w [(1 -a) \ - 2ecrd/_^2ga J Aj e^''^'' , 



J = -jcra^g [2e j aj + 7- 1] AjC ^ , 



P = jqa2/32cvjg [2ecraj - j (7- cr)] Aj e^'^i' 



5^ = -1 



u = , ■' ' ' ; ' 



V = -aoj[{l-a) S- 2ea/32gaj] A3e'^^i'' , 



X = oj [l-o-) \- 2eaS/32gaj] Aje'^^^'' , 



3" = -3cra2g [2ejaj + 7- 1] A3 e ^ , 



P= j q a2/32,.jg [2£craj - j(7-cr)]A3e ^ . ; 



Morfe // (Neglected terms are of the order of (5'^co) 



X = 1 



^2a2 



; c = Vj' 



eap'g- 



1 + 



3 /^g 



2jc^ (1 - a) jw 2jw \2 



U - R-i 



jc.j(l-a) + -^ Vj 



V j ^^ + — 



2co 



OR /^ — 



1 /s 



2ea/32g' 



1 - CT J 



B e(5e/2a>)x g^2' 



V = g- 



jaj(l-a) + -^ VT 



ja 



J-^-' + o 



1 /'5 



2ea-/32g: 

 1 - a 





2w 



Bje(5g/2c.)xg^2' 



<^g 



2z]oj + ( 7- 1 + 2e -2^) VjTJ 

 717 



B^e(Sg/2aOx ^^2" _ 



