B • TURBULENT FLOW 



It is, of course, not uncommon to find empirical formulas with enough 

 adjustable constants to fit experimental results. In the present case, how- 

 ever, the formula, with a specified function o}{y/8) and constants previ- 

 ously specified in the law of the wall, stands the test of a wide variety of 

 conditions. In addition the present similarity law appears to be based on 

 meaningful physical concepts, which may be described as follows. 



It is easily seen that a wake is a natural consequence of earlier fric- 

 tional constraints no matter how they may have arisen. There is therefore 

 coming from upstream a flow of wakelike character, modified obviously 

 by the remnant of upstream effects which caused it and by the local 

 effects which distort the profile so that the velocity approaches zero at 

 the wall. The remarkable thing was that Coles could extract S-shaped 

 profiles typical of the pure wake component. 



Fig. B,21b. Mean velocity profiles of hypothetical 

 boundary layer, after Coles [85]. 



No claim is made that the turbulent structure is the same as that of 

 a real wake. From the limited information available it appears that wake 

 structure is coarser (has larger eddies) than boundary layer structure. 

 However, the law of the wake may be interpreted as a manifestation of 

 a large scale mixing process in which stress-controlling motions are inde- 

 pendent of viscous effects. The wall effect, as we already know, superposes 

 a viscous effect which increases in magnitude as the wall is approached. 



The concept is best illustrated by the diagram of a hypothetical 

 boundary layer used by Coles, reproduced here in Fig. B,21b. The figure 

 shows velocity profiles for various values of a; in a flow proceeding from 

 separation to separation through a region of attached flow. The dashed 

 lines denote the wakelike component represented by the function u){y/8). 

 At points of separation or reattachment we find the wake component 

 only. In regions of attachment we see the effect of the wall friction, and 

 the requirement of vanishing velocity at the wall being met by a sharp 

 drop to zero at the wall. 



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