(x ~ ^ X <*<**** 



Figure 4. 



This briefly summarizes some of the experimental data. The 3-dimensionality 

 that I have been talking about was eventually traced to small span-wise variations in 

 the mean flow in the boundary layer, which when coupled with the circumstance 

 that the frequency of the primary wave was near branch II of the neutral curve, gave 

 rise to local variations in the amplification rate. In fact by choosing a frequency near 

 branch I of the neutral curve the peaks and hollows could be reversed. The 3-dimen- 

 sional character is of practical significance inasmuch as the frequency selected for 

 amplification in natural transition lies near branch II and would be especially susceptible 

 to irregularities in the mean flow. Also a random input would give rise to distorted 

 waves. Although the results obtained to date indicate the presence of 3-dimensionality 

 prior to transition the question as to whether it is an inherent part of the transition 

 process has not as yet been resolved. In this connection it should be mentioned that 

 Hama at the University of Maryland, conducted an investigation of transition on a 

 flat plate in water, using dye and a trip wire and concluded that distortion in the wave 

 always occurs prior to transition. The difficulty has been in getting a flow free of 

 irregularities. Span-wise variations in mean velocity on the order of a few percent 

 appear to be significant. The results obtained do not exclude the possibility of break- 

 down of a 2-dimensional wave, nor exclude the usefulness of a 2-dimensional finite 

 amplitude theory. 



C. C. Lin 



I wish to thank Dr. Wasow for this able comparison between his work and 

 our present approach. It may be well to emphasize that the connection coefficients 

 C v (z, X) are independent of the particular solutions », while kj(z) depends on the 

 index /'. The appropriateness and desirability of using the form 



= 2 C„(*,A)w<"> 



(29) 



370 



