sufficiently high that the results obtained should be typical of high 

 Reynolds number thick stern turbulent boundary layer flows. 



TURBULENT LENGTH SCALE IN THICK STERN BOUNDARY LAYER 

 The experimentally derived mixing length data in the thick stern 

 boundary layers of Afterbodies 1, 2, and 5 indicate that the mixing-length 

 scale is proportional to the square root of the annular area between the 

 body surface and the edge of the boundary layer. It is of fundamental 

 interest to perform an independent and more direct measurement of the 

 turbulence length scale to support this empirical result. The spatial 

 correlation coefficient of two axial velocity fluctuations at points A and 



B (d ) = u'u'/(/ u' / u ' ), as a function of the radial separation 

 ' AB r A B A B 



distance between the points A and B, d = r^ - r^, is chosen for this 

 purpose. The axial velocities at points A and B were measured by position- 

 ing two single-element TSI (Model 1212) hot-wire probes with 90-deg bends 

 at the two points. The linearized outputs of the velocities from the two- 

 channel TSI (Model 1050-1) hot-wire anemometer were a.c. coupled by using 

 an amplifier with low frequency rolloff set at 1 Hz. The fluctuating 



velocity correlation u'u' was then measured by a TSI Correlator (Model 



1015C) . The spatial correlation coefficients were measured at various 



axial locations in the thick stern boundary layer of Afterbody 5. At 



each axial location, point A was fixed at r = r^ + 0.167 6 and the radial 



location (r >r.) of point B was increased until the value of p became 

 B A '^^ 



"small." 



The measured spatial correlation coefficients are plotted in Figure 15 

 (data are tabulated in Table 5) against three nondimensional length 



/ 2 2 * 



parameters, namely, n = d // (r^+d ) -r^, d^/6^, and d^/6 . As shown in 



Figure 15, the measured correlation coefficients at various axial locations 



are not similar when ri is taken to be d /6 or d /6 ; the correlation 



length scale of the turbulence in the thick stern boundary layer is not 



proportional to the local radial boundary-layer thickness 6 or the planar 



displacement thickness 6 . However, it is interesting to note that the 



P 



44 



