A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



and it is not yet clear whether we can recognize a single process as active 

 in all the varied manifestations of beginning turbulence. Various ap- 

 proaches have been made by various investigators in the search for a 

 key principle or idea which will unlock the door leading to understanding. 

 Controversies have developed as to the adequacy of hnear theories to 

 contribute to a solution of the problem, especially as to the role of the 

 linearized theory of the instability of laminar flow. Nevertheless it seems 

 to me that, although a large amount of experimental and theoretical work 

 remains to be accomplished, the principal outlines are reasonably clear 

 and the apparently rival ideas are not contradictory but complementary. 

 The phenomena are, however, far from simple. 



For very small free stream turbulence, small surface roughness, and 

 bodies of large fineness ratio, transition is preceded by the selective ampli- 

 fication of the small disturbances present. The process in the early stages, 

 which is well described by a linear theory, is usually described as an 

 instability. However, the linear theory describes only the amplification 

 of disturbances, and if no disturbance is present, no oscillations result. 

 The oscillations do not continue after their production if the disturbances 

 are removed. The linear theory gives the result that viscosity produces a 

 phase shift between the tangential and normal components of the velocity 

 fluctuations which gives rise to shearing stresses which in turn modify 

 the original velocity distribution. Hence, some of Munk's criticisms [123] 

 of the linear theory are not justified; it is true, as will be seen later, that 

 the linear theory cannot describe the transition process itself. The hnear 

 theory is well established both theoretically and experimentally as de- 

 scribing the beginning of the process leading to transition when the dis- 

 turbances are small. 



The initial disturbances to be introduced into the linear theory arise 

 from several sources; collectively they may be described by a composite 

 spectrum of intensity and frequency made up of several components, as 

 follows: (1) the initial turbulence of the air stream, (2) acoustic waves, 

 (3) the disturbance at the nose or leading edge, and (4) disturbances due 

 to roughness and shock waves from external sources. Since the wave- 

 lengths of the most highly amplified waves are much larger than the 

 thickness of the boundary layer, we may be justified in considering only 

 the frequency region corresponding to wavelengths longer than the bound- 

 ary layer thickness and to consider that all sources of disturbance yield a 

 spectrum of velocity fluctuations superposed on the free stream velocity. 

 Whether this simphfication is justified or not is a matter for further 

 investigation. 



The initial turbulence of the air stream enters directly as a series of 

 randomly varying disturbances of the free stream flow. Acoustic waves 

 produce particle motions which in most cases are comparable with a very 

 small initial turbulence (a few hundredths of one per cent) and, hence, 



(68 ) 



