A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



to give a typical error-law distribution of vorticity across the wake a short 

 distance downstream from the cyhnder [37]. 



Accordingly, transition should not be defined as breakdown of laminar 

 flow but as the onset of the highly diffuse turbulent motion of random 

 character. 



A, 10. Tentative Conceptual Picture of Transition. The account 



that has been given of the several typical flow situations in which tran- 

 sition is recognizable and of the influence of many of the controlling 

 variables suggests that we are dealing with an effect which may have 

 many causes. Each variable, initial turbulence, pressure gradient, rough- 

 ness, in the absence of the influence of the other variables, fixes transition 

 at a definite location for a given Reynolds number of the body. That 

 variable which gives the most forward location of transition is the one 

 which will be the controlling one under the given set of circumstances. 

 Thus any of the variables may be controlling depending on the values of 

 the other variables. If the initial turbulence and roughness are sufficiently 

 small, transition will be preceded by regular Tollmien-Schlichting oscil- 

 lations of increasing amplitude. 



There has been considerable progress in understanding the breakdown 

 of laminar flow as a result of the theoretical and experimental work on 

 the stability of laminar flow as described in IV,F. There is, however, no 

 mathematical theory of the transition process itself. A satisfactory mathe- 

 matical theory most certainly will have to take into account the nonlinear 

 terms in the equations of motion of a viscous fluid. A great deal of experi- 

 mental material is available. In most of the experiments essential measure- 

 ments of the controlling variables were not made; especially lacking are 

 measurements of the intensity and scale of the initial turbulence of the 

 fluid stream which is now known to be one of the most important con- 

 trolling factors. In other cases the surface roughness and waviness are not 

 known. For the most part the experiments were made in the absence of 

 any guiding theory. For all these reasons it is exceptionally difficult to 

 systematize and analyze the data. 



During the course of the past 15 years as the experimental data accu- 

 mulated, new physical aspects of the phenomena have unfolded and sug- 

 gestions as to a descriptive physical mechanism have come to mind. It has 

 been suggested that an immediate prerequisite in every case is separation 

 with the resulting formation of a free shear layer within the boundary 

 layer or shear layer under observation, the scale of the newly formed 

 shear layer being an order of magnitude lower than that of the layer 

 under study. This separation is presumed to occur even when the appar- 

 ent dominating experimental variables are initial turbulence or surface 

 roughness. Like the progression of eddies of successively decreasing size 

 in the modern theory of turbulence bounded at the lower end by eddies 



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