Discussion 



M. A. WEISSMAN 



109 



My question was "What is your definition of 

 growth rate?" This is quite a crucial point, for 

 in comparing theory to experiment, we must make 

 sure that we are comparing like to like. 



The meaning of growth rate for nonparallel 

 flow is not obvious. Let us consider El-Hady and 

 Nayfeh's lowest order solution (Eq. 42): 



z = A C(x ,y)exp[ij(a + ca )dx 

 10 1 1 



iut] (1) 



The downstream growth of the magnitude of this 

 function is not purely contained in the expotential 

 factor. The change in the eigenf unction, C, with 

 X also contributes to "growth." In fact, a com- 

 plete definition of growth would be 



G = 





using (1) , where it is understood that a. and a. 

 are the negative and imaginary parts of a^ and a,. 

 [Bouthier (1972), Gaster (1974), and Eagles and 

 Weissman (1975) ] . 



Equation 2 shows that the growth rate is 

 actually a function of y. (It is also a function 

 of the flow quantity under consideration, see the 

 above mentioned references.) However, if^ we agree 

 to measure the growth rate at a particular 

 y-position and i£ the eigenfunction is normalized 

 at that position (so that 3|c|/3x = at that 

 position) , then the influence of the changing 

 eigenfunction on growth rate will disappear (for 

 this particular definition of growth rate ) . The 

 poit is that a. is not uniquely defined; it depends 

 on the normalization used for ?. [This can also 

 be seen from examination of the equation defining 

 a. , Eq. 35] . The authors have neglected to explain 

 what their normalization was. 



which reduces to 



REFERENCES 



"O "^ ^"l "" 



1 3|i;| 



Eagles, P. M. , and M. A. Weissman (1975). On the 

 (2) Stability of Slowly Varying Flow. J. Fluid. Meah. 

 69, 241-262. 



