122 



0.5 6 7 8 9 1,0 



FIGURE 5(e). Boundary layer thickness. 



2 



L 



(kIO^) 



Aj I 

 0.5 



5 6 



FIGURE 5(f). Planar And axisymmetric momentum deficits. 



0.5 0,6 0,7 



08 



09 1,0 



6 0,7 OB 0.9 

 X/, 



1,0 



FIGURE 5(g). Shape parameter. 



FIGURE 5(h). Wall shear stress. 



to the axis for the wake. In the interest of clar- 

 ity, the results of all the calculations (cases A 

 through E) are shown only at one axial station 

 (Figure 4b and 5b) , those at other stations being 

 qualitatively similar. 



Considering the most detailed figures, 4b and 

 5b, first, it is clear that the predictions are 

 rather poor when the length scale, £, is assumed 

 to be the same as that in a thin boundary layer 

 (case A) . This is particularly evident in the pre- 

 diction of the shear-stress profiles across the 

 boundary layer and the near wake. Incorporation 

 of the correction to I to account for the extra 

 rate of strain due to longitudinal curvature (case 

 B) leads to a marginal improvement in the case of 

 the low-drag body and a dramatic improvement for 

 the modified spheroid. This is to be expected in 

 view of the grossly different surface curvature 

 histories of the two bodies as noted earlier 



(Figure 2). Nevertheless, it is clear that this 

 correction by itself is not sufficient to account 

 for the differences between the data and the calcu- 

 lations with thin boundary-layer turbulence models 



(case A) . The application of the correction for 

 the extra rate of strain due to the transverse 

 curvature (case C) appears to account for a major 

 portion of these differences for both bodies. The 

 influence of transverse curvature is in fact seen 

 to be somewhat larger for the low-drag body as 

 would be expected from the fact that 6/rQ is greater 

 in that case (Figure 2) . The simple addition of 

 the effects of the two rates of strain (case D) 

 leads to a significant improvement in the prediction 

 of both the velocity profiles and the shear stress 

 profiles. The incorporation of a variable pressure 

 gradient across the boundary layer (case E) , which 

 is an attempt to account for the normal pressure 

 gradients, appears to make a significant improve- 



