A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



the Reynolds number was increased. This behavior is typical of tran- 

 sition. Fig. A, 7 shows the results obtained at three Reynolds numbers. 

 The boundaries of the shear layer were determined as the point at which 

 the Pitot pressure "begins to decrease" and the point at which the Pitot 

 pressure "reaches a constant minimum value." The critical Reynolds 

 number for transition based on this thickness varied systematically with 

 the Reynolds number of the cylinder, increasing from 510 at a cylinder 

 Reynolds number of 3540 to 900 at a cylinder Reynolds number of 8540. 

 A most important observation was that a disturbance introduced by a 

 wire of small diameter in the boundary layer of the cylinder moved the 

 transition closer to the cylinder. Hence the transition of a laminar shear 

 layer is a function of the initial turbulence as is transition in a boundary 

 layer. 



Re = 5000 



Rer= 14,480 



Re = 8540 



x/D 



X = distance from cylinder 

 Fig. A,7. Free shear layers behind a circular cylinder exhibiting transition. 



The shear layer behind the cylinder is subjected to pressure gradients. 

 However, no accurate static pressure measurements could be made in the 

 wake. The total pressure along the plane of symmetry of the wake falls to 

 a minimum at the point where the shear layers from the two sides meet. 

 The shear layers are not very thin and probably the static pressure is not 

 constant across them. However, the rising value of the critical Reynolds 

 number of the shear layer and the more rapid fall of the total pressure 

 along the plane of symmetry of the wake suggests that transition in a 

 shear layer may be delayed by a favorable pressure gradient as in the 

 case of a boundary layer. 



Schiller and Linke do not give their data in sufficient detail to permit 

 an accurate calculation of the displacement thickness which in this case 

 might be defined by the relation 



(i/e — Ua)b* = / {u — Uo)dij 



where Wo is the velocity at the inner boundary. As a rough guess 3* is of 

 the order of 0.3 the thickness defined by Schiller and Linke, and hence 

 Res* is of the order of 150 to 270 at the turbulence of Schiller and Linke's 



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