B,28 • GENERAL FORM AND STRUCTURE 



the round jet this is usually between 0.5 and 1.5 orifice diameters down- 

 stream from the orifice. The virtual origin appears to be less well defined 

 for the plane wake and is different for the extrapolated center velocity 

 than for the extrapolated width (Townsend [1]). 



The foregoing relations apply as long as the Reynolds number remains 

 sufficiently high for similarity to exist. Since the Reynolds number is pro- 

 portional to x'^~'^, it is seen from Table B,27 that, if the condition is 

 initially satisfied, it will continue to be satisfied with ever-increasing x 

 in all cases, with the exception of the round wake. For the latter the 

 Reynolds number will eventually decrease to the point where the turbu- 

 lent laws of spreading and decay merge into laminar laws with a new 

 virtual origin. The distances for this change to occur can be expected to 

 be very great, and in most cases any practical interest in the wake will 

 have already been lost. 



As already indicated, it is required in the foregoing analyses that 

 similarity extend to the turbulent motions responsible for diffusion. The 

 same rules must therefore apply to the scales of length and velocity enter- 

 ing into the diffusion process. If we adopt the concept of eddy viscosity, 

 we may compare the behavior of a turbulent flow to that of a laminar 

 flow in terms of the behavior of a viscosity. Denoting the mean eddy vis- 

 cosity applicable to the flow by e^, we have, since e^ is proportional to a 

 length times a velocity. 



Referring to Table B,27, we find that e^ is constant for the round jet and 

 the plane wake. These flows should then behave as laminar flows with 

 respect to their form of spreading and decay, as in fact they do. It must 

 be borne in mind that we are here concerned only with the proportionality 

 rule, not with absolute magnitudes. In the case of the plane jet, e^, in- 

 creases as x^j and we find, as we should, that the spreading and decay 

 follow faster laws than those governing laminar flow. In this case the 

 laminar exponents are 



In the case of the round wake, e^j decreases as x~^, and we find, again as 

 we should, that the spreading and decay follow slower laws than those 

 governing laminar flow. Here the laminar exponents are 



B,28. General Form and Structure. The boundary which separates 

 the turbulent fluid, of say a jet or a wake, from the nonturbulent sur- 

 rounding fluid is determined only by how far the motions have pene- 

 trated the surroundings. While it is self-evident that the boundary must 

 be irregular, it was not until comparatively recent hot wire studies were 



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