Figure I . Turbulent wake of bullet. 



[courtesy of Ballistic Research Laboratory, Aberdeen Proving 

 Grounds] 



Inequalities like 



can be gotten in principal by setting 



dvi dv t 



Vj — « u k — 



dxj dx k 



v k ' « u k ' , 



(1) 



(2) 



but the static pressure contribution of v- h to the Navier-Stokes equation will probably 

 behave like 



p v ~ pUvj 



(3) 



so that the inequality (2) may be insufficient to permit neglecting static pressure 

 effects.* Nevertheless, if we can devise a convenient quantitative representation for 

 static pressure perturbation, there is some hope of exploiting a point source method. 



The foregoing matter is carried no farther here. This paper deals instead with 

 some traditional shear flows such as boundary layer, channel, wake and jet — especially 

 in terms of shear stress, strain-rate and their fluctuations. 



The Proximity of Boundaries in Turbulent Shear Flows 



In theoretical analysis of turbulence, restriction to homogeneity brings con- 

 siderable simplification, and such an approach is being made to shear flow by Reis and 

 Lin [3] and by Burgers and Mitchner [4]. Homogeneity, the invariance to translation 

 of all statistical properties of the turbulence, requires that the boundaries be at infinity, 

 or at least far apart compared with the maximum correlation distance of the fluctua- 

 tions. To evaluate the possible role of a theory of homogeneous shear flow, it is 

 instructive to recall some pertinent experimental results. 



Figure 1 is a shadowgraph of the wake of a supersonic bullet, several hundred 

 diameters downstream. In the ballistic range the camera is fixed with respect to the 

 undisturbed air, and at this station all velocities are far below sonic. The wake is 

 visible because of residual temperature fluctuations in the turbulence. Of interest here 



Townsend appears to disagree: [1], p. 57. 



374 



