Theory of Turbulent Flow Between Parallel Plates 



P = dimensionless fluctuating pressure - 



Jj = dimensionless temperature amplitude indexed by « 

 (when written in fluctuation equation sets, the 1 sub- 

 script may be omitted but is understood) 



Pj = dimensionless pressure amplitude indexed by w (when 

 written in fluctuation equation sets, the 1 subscript may 

 be omitted but is understood) 



u,v,w = the dimensionless x, y, z velocity amplitudes for a par- 

 ticular fluctuation indexed by w. 



q = 1/3 + A-^./Moo 



u'^.y^ = dimensionless variables based on the friction velocity 



i/- = a functional form (= w + i R^ ) 



Mp = a constant indexed by ^^j (= w + SR^q) 



a = indifferently used to represent a constant 



x,Y,z = dimensionless amplitudes representing the fluctuating 

 components of vorticity, indexed by ^. 



b ,b ,b ,d = characteristic functions in the core (dimensionless — 



12 3 4 ^j^,,^ ^jt,^.^ ^ib3X^ ^d,x) 



(J,®,C,® = amplitudes for core solutions 



a ,c a c = characteristic functions in the boundary layer 

 (dimensionless- e^^'% e<^2% e^"^-, e^^'^) 



A, B, c, D = amplitudes for boundary-layer solutions ' '■ ' 



I = wavelength 



s = Strouhal number 



APPENDIX - SOME FINAL COMMENTS 



Since a number of readers were satisfied with the results obtained in the 

 secular equation, but did not consider the argument by which boundary conditions 

 were satisfied only for a single set at each wall (namely, for the incoming wave 

 system, and not the dual incoming and outgoing system) fully transparent, it 

 seems desirable to suggest how the result may be obtained by functions which 

 are continuous across the entire section. This requires a suitable open form 



737 



