B,27 • LAWS OF MEAN SPREADING AND DECAY 



turbulence) exceeds the growth in diameter, and the Reynolds number 

 tends toward an eventual zero value. 



We are therefore dealing with a class of flows in which the effects of 

 viscosity are removed from those turbulent motions which control the 

 mean motion and are relegated to the small scale eddies which take part 

 in the final decay and the production of heat. In this respect the flow 

 fields are subject to a controlling mechanism similar to that found in the 

 outer regions of a turbulent boundary layer, but lacking the influence of 

 a wall such as prevails to varying degrees in the boundary layer. Once the 

 flows have attained a fully developed state, they remain similar through- 

 out upon subsequent development, merely changing scales of length and 

 intensive properties. 



The fully developed state is an asymptotic condition reached only at 

 some distance from a body in the case of a wake and from a nozzle in 

 the case of a jet. Since the initial conditions in these two cases are vastly 

 different, the distance for their effect to disappear is also different. Behind 

 a body the flow is highly agitated by a succession of eddies comparable to 

 the diameter of the body, and this coarse scale motion persists for a long 

 distance. Townsend [108], in his investigation of the plane wake behind 

 a cylinder, finds that the mean wake flow reaches similarity only after 

 100 cylinder diameters downstream, and that complete statistical equi- 

 librium in the turbulent motions is not reached short of 1000 diameters. 

 At a nozzle the initial jet consists of a potential core of relatively smooth 

 flow, or a flow characteristic of the internal flow, bounded by a layer in 

 which free mixing begins. Kuethe [109] finds that the potential core of a 

 round jet is consumed between 4 and 5 nozzle diameters downstream of 

 the plane of the nozzle, and that fully developed jet flow is estabhshed at 

 8 nozzle diameters. 



We shall here be concerned mainly with fully developed character- 

 istics and shall attempt to describe the principal ones, paying most atten- 

 tion to the plane wake (two-dimensional) and the round jet (axially 

 symmetric) since these have been investigated in the most detail. Since 

 little information is available on the wake of a seff-propelled body, this 

 case will not be considered. A discussion of its laws of spreading and 

 decay may be found in [110]. 



B,27. Laws of Mean Spreading and Decay. A certain amount of 

 useful information can be gathered from the equations of mean motion 

 without requiring their actual solution. Using the condition that momen- 

 tum, heat, and matter are conserved and that the flow when fully devel- 

 oped preserves similarity among mean motions and those turbulent mo- 

 tions which influence the mean motion, it is possible to obtain the laws of 

 spreading and decay of mean properties. 



The conventional procedure, which will be followed here, is to assume 



( 159) 



