Author's Reply 



ELI RESHOTKO 



49 



Dr. Gazley and his colleagues have long been 

 interested and active in the topic of heated 

 boundary layers and his comments on the conse- 

 quences of power-law temperature distributions 

 are greatly appreciated. 



Let me first restate our experimental results. 

 Referring to Figure 17 of the paper, our experi- 

 ments for At < 8°F appear to indicate decreased 

 amplification rates as the exponent n decreases 

 toward zero and in fact for some range of negative 

 values of n, the disturbances become damped. In 

 the temperature range AT < 8°F, neither our cal- 

 culations (cited in the paper) nor Gazley' s give 

 any basis for this experimental result. 



Nayfeh and El-Hady (private communication) 

 have recently pointed out that water boundary 

 layers with non-isothermal walls cannot have 

 similar boundary layer solutions because of the 

 variable properties of water. They show that if 

 one first calculates the non-similar boundary 

 layer profiles expected at the measuring station 

 of the Strazisar-Reshotko experiments and then 

 analyzes the stability of these profiles , the 

 resulting growth rates are qualitatively in accord 

 with the Strazisar-Reshotko results as shown in 

 the figure below supplied to me by Professor 

 Nayfeh. Note in the figure that as n decreases, 

 the growth rates also decrease, and although the 

 calculated maximum growth rates are not negative 

 for the non-parallel calculations with n = -0.5, 

 they are very close to zero. This trend is oppo- 

 site to what was obtained for the stability of 

 similar boundary layer mean profiles. 



Nayfeh and El-Hady 's calculations do not go 

 beyond AT = 8°F. But I believe that they have 

 made their point that when studying the stability 

 of water boundary layers with power- law or other 

 non- isothermal wall temperature distributions, 

 one must analyze the stability of the appropriate 

 non-similar boundary layer profiles in order to 

 obtain even the correct qualitative trends. 

 Therefore I believe that the results presented by 

 Dr. Gazley in his comment must be reexamined. 



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FREQUENCY F x|0^ 



Effect of power law wall heating on stability of non- 

 similar water boundary layer. parallel, non- 

 parallel, a = Im (a + eaj) where a is the quasi- 

 parallel amplification rate and eoj is the non-parallel 

 contribution. 



