A, 7 • SHEAR LAYERS IN THE FREE FLUID 



of 5 is equal to 1.345* and for the Pohlhausen 4-term approximations to 

 flows with pressure gradient the NACA value of 5 is 1.28 and 1.325* for 

 values of X = 12 and — 12. The value of Re^* for transition is often con- 

 verted to an equivalent flat plate value of Re^, by the approximate relation 

 Re = ^Re^i*. The values of Re^* at transition on a smooth flat plate with 

 zero pressure gradient vary from 515 to 2900 corresponding to the values 

 of Re^ of 9 X 10^ to 2.8 X 10^ previously quoted. A plot of Re^* against 

 intensity of turbulence is shown in Fig. A,6. 



A, 7. Transition of Shear Layers in the Free Fluid. Another of 

 the frequently observed characteristic phenomena in addition to tran- 

 sition is that of separation of the flow from a solid boundary and we shall 

 see that there is an interplay between the two phenomena. Separation of 

 the flow is accompanied by a reversal in the direction of the flow very 

 close to the boundary behind the separation line and by the formation 

 of a wake in which the velocity is much reduced. Separation is a boundary 

 layer phenomenon ; it occurs when the pressure increases in the downstream 

 direction, or in our previous terminology, when the boundary layer en- 

 counters an adverse pressure gradient of sufficient magnitude. When the 

 pressure rises, the flow in the boundary layer is retarded by the pressure 

 as well as by the surface friction and the fluid near the surface is ulti- 

 mately brought to rest. When separation occurs, the boundary layer be- 

 comes a shear layer in the free fluid, sometimes called a vortex layer. 

 Such shear regions in which the velocity gradient is much larger than 

 elsewhere are found where discontinuities of velocity, or of the physical 

 properties of the fluid are introduced, as for example, in the case of a 

 jet of fluid issuing in a surrounding quiescent fluid. 



The flow in such a shear layer may be laminar or turbulent and tran- 

 sition is observed to occur in shear layers as well as in boundary layers. 

 An early rule of thumb was that if the Reynolds number formed from the 

 velocity at the outer edge of a boundary layer and its thickness were less 

 than about 2000, transition would not occur. However, shear layers are 

 much more unstable (IV, F) and transition has been observed at Reynolds 

 numbers less than 100. Thus a laminar boundary layer often exhibits 

 transition immediately following separation. 



If the Reynolds number is sufficiently low a laminar boundary layer 

 may separate and continue as a laminar shear layer for a considerable 

 distance. Transition in such a laminar shear layer has been studied in 

 some detail by Schiller and Linke [24,25]. The shear layer was found in 

 the flow field around a circular cylinder at Reynolds numbers (based on 

 cylinder diameter) of 2000 to 20,000. Pitot tube traverses of the wake 

 showed the existence of a shear layer proceeding from the separating 

 laminar boundary layer. Its thickness increased relatively slowly and then 

 much more rapidly at a line which approached the line of separation as 



<21 ) 



