144 



Shaw et al. (1967) argue that the turbulence energy 

 equation can be used to model the memory effect. 

 In order to determine the rate of change of tur- 

 bulent intensity along a mean streamline, three 

 assumptions have to be made: namely, that turbu- 

 lence intensity is directly proportional to the 

 local Reynolds stress, a^ = -u' v'/q^ = 0.15; that 

 the dissipation rate is determined by the local 

 Reynolds stress and a length scale depending on 

 n/6 ; and the energy diffusion is directly pro- 

 portional to the local Reynolds stress with a fac- 

 tor depending on the mixing value of Reynolds stress. 

 On the basis of thin boundary- layer data two em- 

 pirical functions for the last two assumptions were 

 proposed by Bradshaw et al. (1957) . The first as- 

 sumption, 11/6 = f 1 (n/6) , was found not to be 



applicable to the present thick axisymmetric stern 

 boundary layers. The deviation of the apparent 

 mixing length along the curved boundary from that 

 of a thin flat boundary was also noted and dis- 

 cussed by Bradshaw (1969) . A simple linear cor- 

 rection to the length scale of the turbulence by 

 the extra rate of strain was made by Bradshaw (1973) . 

 The extension of this concept has just been made for 

 the thick axisymmetric boundary layer by Patel et 

 al. (1978). 



It is important to note that the boundary- layer 

 thickness of a typical axisymmetric body increases 

 drastically at the stern. Most of the rapid change 

 takes place within a streamwise distance of a few 

 boundary-layer thicknesses. Most of the empirical 

 functions for solving the turbulence energy equa- 



FIGURE 18. Measured distribu- 

 tions of eddy viscosity for 

 afterbody 2 . 



0.018 



0.016 



0.014 



0.012 — /(77 



0.010 



* P 0.008 



0.006 



I ^ 1 Qa 



0.2 



0.6 0.8 

 r — r„ 



0.10 



0.08 



0.06 



0.04 



0.02 



fIGUKi; 19. Measured distribu- 

 tions of mixing length for 

 afterbody 1. 



0.2 



0.4 



0.6 



0.8 



1.0 



1.2 



1.4 



