Fabula 



incipient overlap of the macromolecular coils in the solution at rest, since ap- 

 proximate theoretical calculations give that value as roughly a few hundred ppm. 

 Thus, if entanglements are formed at much lower concentrations, the relative 

 motion of the coils and their deformation due to flow may also be involved. 



In connection with Dr. Gadd's suggestion that small eddy suppression is 

 perhaps irrelevant to turbulent drag reduction, Tu and Willmarth remark* that 

 "small eddies near the wall may become larger when they distend into the more 

 central region." Thus, perhaps the small-eddy suppression phenomenon in free 

 jets discovered by Dr. Gadd is relevant but depends on flow parameters as well 

 as concentration. 



Professor Hummel's note of the probable importance of the high polarity of 

 water molecules to entangliement is very important, and it may be desirable to 

 use other solvents for that or other reasons. In some work under Professor 

 J. L. Zakin at the University of Missouri, Rolla, wedge hot-film velocity sensors 

 in high-polymer organic solvent solutions have not shown the abnormal calibra- 

 tion behavior found in Polyox aqueous solutions in this work. 



Professor Hummel's suggestion that macromolecules could act to stabilize 

 vortices is intriguing, since such a mechanism could be important to the turbu- 

 lent friction reduction effect by reducing turbulent energy production. t However, 

 his suggestion that such stabilized vortices could contribute to the signal rag- 

 gedness in the grid turbulence experiment does not seem to be supported by the 

 observations. One can predict from vortex shedding observations the order of 

 magnitude of the expected spacing for those vortices, and one can detect the 

 major vortices as individual dimples on the water surface behind the grid. In 

 both ways a spacing of the order of several centimeters is obtained for these 

 tests. If the signal raggedness were to be associated mainly with such vortices, 

 the raggedness would be expected to come in random bursts with an average 

 spacing corresponding to several centimeters of sensor travel. Since the sen- 

 sor travel during a typical sweep in the waveform photographs is about 3.6 cm, 

 only one or two bursts would be expected per sweep. In fact, however, the rag- 

 gedness is quite uniformly distributed over most sweeps. Thus, there seems to 

 be no discernible evidence of the suggested behavior in this work. 



*B.-J. Tu and W.W. Willmarth, "An Experimental Study of the Structure of Tur- 

 bulence Near the Wall Through Correlation Measurements in a Thick Turbulent 

 Boundary Layer," University of Michigan, Dept. of Aerospace Eng. Tech. Rep. 

 02930-T, 1966. 



'A.G. Fabula, J.L. Lumley, and W.D. Taylor, "Some Interpretations of the Toms 

 Effect," in "Modern Developments in the Mechanics of Continua," Acadennic 

 Press, New York, 1966. 



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