XIV 

 ON THE STABILITY OF THE LAMINAR BOUNDARY LAYER 



C. C. Lin 

 Massachusetts Institute of Technology 



1 . Introduction 



This paper was originally intended to contain only a discussion of a new treat- 

 ment of the central mathematical problem arising in the theory of stability of parallel 

 flows. However, at the suggestion of the organizers of the Symposium, there is also 

 included a brief survey of other aspects of the stability of the boundary layer and its 

 transition to turbulence. 



As is well known, when the speed of fluid motion is sufficiently high, it in general 

 becomes fluctuating and turbulent even when the external conditions are steady. This 

 is to be expected if one regards a body of fluid as a mechanical system with an infinite 

 number of degrees of freedom. It is only when frictional forces are large, i.e., when the 

 Reynolds number is sufficiently low that most of the possible modes of motion are 

 damped out, resulting in the laminar flow. 



The practical engineer is deeply interested in the problem of transition between 

 laminar and turbulent flows because, among other things, turbulent flows are associated 

 with much larger energy losses, and it is often desirable to try to avoid it (although in 

 chemical engineering, it is sometimes desirable to promote turbulent mixing). 



Unfortunately, with the present status of our knowledge, it is impossible to pre- 

 dict, with any great degree of certainty, the point of transition between laminar and 

 turbulent flow in a boundary layer (say) under a given set of flow conditions. One 

 reason for this is the large number of factors that enter into the determination of transi- 

 tion; e.g., 



1. turbulence and noise in the free stream, 



2. roughness of the surface, 



3. curvature of the surface, 



4. pressure distribution along the surface, 



5. temperature of the surface. 



However, through theoretical and experimental investigations, it has often been found 

 possible to define proper dimensionless parameters for describing the influence of the 

 various factors. Still, it would be very difficult to devise any comprehensive experi- 

 mental program to include all these factors, and many others, e.g., compressibility, 

 surface suction, etc. It thus appears that a sensible approach is to study the effect of 

 varying the individual factors when other conditions are kept unchanged, and, at the 

 same time, to try to understand the basic mechanism of transition. In this way, we may 

 hope to be better prepared to cope with a given situation. 



In Section 5, I shall return to the discussion of the effect of some of the above 

 factors on transition. For the moment, let us consider briefly the inherent instability of 

 the laminar flow and the growth of the small disturbances. Such processes are certainly 

 of primary importance if we wish to understand the basic mechanism of transition. 



2. Instability of laminar flow 



It is now known that the instability of the laminar flow with respect to small 

 disturbances does not always play the dominant role in a given transition phenomenon. 



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