16 



lower critical Reynolds number computed from this theory. The theory does not 

 relate the onset of instability to surface roughness, nor predict the magni- 

 tude of the velocity fluctuations produced. However, the mathematical work 

 clearly shows that only certain disturbances at sufficiently high Reynolds 

 numbers will produce instability and also predicts the effect of pressure 

 gradients on the stability of the flow. Many of the results obtained from the 

 tests on the tanker model may be interpreted in the light of this theory. 



QUALITATIVE ANALYSIS 



Condition 1 - No Stimulation 



The qualitative analyses of the boundary-layer flow on the tanker 

 model without any stimulation are summarized in pictorial form in Figure 12. 

 These results show, first of all, that a considerable portion of the wetted 

 surface is covered by laminar flow, 20 percent at 0.5 knot and 3-3 percent at 

 3.5 knots. Further, it appears from the shape of the laminar region that 

 transition occurs earlier near the free surface. Such a condition implies 

 that more destabilizing influences are present here than at points below the 

 surface. Destabilizing effects may conceivably arise from additional vortic- 

 ity generated at the free surface and also from surface waves which may be 

 interpreted, by a Fourier analysis, to contain disturbances of all frequencies. 

 As shown in the preceding section, the stability theory predicts that only 

 certain types of disturbances will cause transition. Hence it appears more 

 likely that with a wide spectrum of disturbance frequencies available to the 

 boundary layer near the surface, transition will occur earlier here. It is 

 expected that such influences as are peculiar to the free surface would decay 

 exponentially with depth so that transition along deeper streamlines would 

 occur farther along the body. 



It must be noted in this case that the outlines of the regions of 

 laminar, transitional, and turbulent flow are approximate because the deter- 

 minations were made at discrete points. For example, no wires were placed 

 very close to the water surface, and hence it is quite possible that there is 

 a strip of transitional and turbulent flow near the surface extending farther 

 forward than indicated in Figure 12. In addition, the boundary-layer patterns 

 are in some instances given for a range of speeds. It is reasonable to assume 

 that these patterns varied within these speed ranges. In view of the fixed 

 hot-wire positions, however, such small changes that may have been present 

 were not detected when they occurred between stations of observation. 



