A. S. Iberall 



ACKNOWLEDGMENTS 



Grateful acknowledgment is due Ralph Cooper and to the office of Naval Re- 

 search for their singular willingness to support this effort; also to the author's 

 colleague Don Young for a continued dialectic on the mathematical issues, and 

 to Dr. D. P. Johnson and Dr. Harry Soodak for reviewing the mathematical- 

 physical questions. :ii - 



NOTATION 



Operators, Indices, Coordinates 



x,y,z = Cartesian coordinates. In any particular context they 

 may have dimensions or be dimensionless (normalized 

 by half separation of the parallel plate channel). When 

 specialized for channel flow, x = the cross-channel 

 coordinate, y = the lateral coordinate, z = the axial 

 coordinate parallel to the mean flow. 



t = time 



i = Subscript representing the Cartesian coordinates. When 

 an index is repeated in a term, it is summed by tensor 

 convention. 



,i = Covariant derivative (= 3/3x.) 



V = Alternatively, boldface is used to denote a vector v. 



i, j,k = Unit vectors 



D = Derivative with respect to x (= d/dx) 



^[ ] = ^[ ]+Vj[ ],3 = total derivative 



V. = i-th component of velocity 



i = ^ 



/^«^ = Time average of the expression spanned by the symbol. 



oo = A subscript that denotes parameters which are constant 

 throughout the field. 



= A subscript that denotes time averaged terms. 



(1) = A subscript that denotes fluctuating terms. 



n = Dimensionless del operator (= hV). 



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