on the ship varies a great deal in thickness from the bow to the stern, close to the pro- 

 pellers, but the streaks are all about the same distance apart, whether at the front or the 

 back. 



It must be closely associated with something close to the boundary, because, for 

 example, there is a wake behind each rivet head. I think this streaky phenomenon is 

 something that occurs very characteristically close to the boundary even in fully devel- 

 oped boundary flows. 



E. Silberman 



The remarks just made (by the previous discusser) bring to mind similar 

 results obtained on the walls of a curved duct. The duct cross section was 6 in. 

 square and the walls were of Lucite. The inner surfaces were coated with a thin paste 

 of aluminum powder in machine oil. The fine streaks mentioned appeared in the oil 

 and apparently took the directions of the streamlines at the walls. (Directions given 

 by the streaks coincided with the limiting directions of fine yarns moved from the 

 interior to the boundary of the fluid.) Observations of the erosion process producing 

 the streaks gave the impression that the paste was first dislodged in a direction other 

 than the streak direction, but almost immediately turned in the streak direction. 

 Reynolds number based on duct hydraulic diameter was about 5 x 10* for the experi- 

 ments. 



G. K. Batchelor 



I don't think these remarks have any bearing on the explanation of the 

 observed streaks of dye. The same phenomenon of longitudinal streaks or ridges on 

 thin films has been observed on aircraft wings smeared with oil, and in fact has 

 been used to make visible the shape of the streamlines of the air flow. I don't think 

 it has been analyzed, but I feel pretty sure it is related to the characteristics of the film 

 itself, and is the result of some kind of instability tending to make the oil move side- 

 ways and gather itself into longitudinal ridges and troughs. I think one can see this 

 as fairly natural if one thinks of the way in which the oil ought to arrange itself in 

 order to have the least amount of viscous dissipation as a result of the shearing action 

 produced by the airflow outside the film, and the fixed wall underneath it. 



In other words, this seems to me to be a film phenomenon, whereas the prob- 

 lem we are talking about is concerned with the flow in the boundary layer itself. 

 Surely the streaks of dye are related to the idea of longitudinal diffusion, which Taylor 

 talked about a few years ago in connection with the dispersion of salt solution in a 

 pipe. He pointed out that if you produce a small cloud of salt solution in turbulent 

 flow in pipe, the variation of mean velocity across the pipe tends to draw out the 

 cloud longitudinally. Wouldn't this also happen here, when Professor Hama's dye is 

 ejected across the flow? Will not the part of the dye that lies farther from the wall 

 also be a part which moves forward more rapidly, thus producing a streak of dye? 



F. R. Hama 



The distinct difference between the streak formation and the non-streaky flow 

 is that, if you don't have the trip, the dye comes out uniformly and no filamentation 

 occurs, and, only when the trip is applied, the wisp formation takes place. Therefore, 

 the wisp formation must have resulted from the secondary spiral flow. 



M. P. Tulin 



Just before Dr. Batchelor got up I was thinking of experiments we (Mr. Ralph 

 Cooper and myself) had made at the Model Basin several years ago, investigating the 

 effects of studs on transition. These measurements were made on a bi-convex, thin 

 plate which was towed in a model basin. Transition was determined by coating the 



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