24 



most important features of the process. Firstly, 

 a clear demonstration of the difference between 

 a purely periodic wave train and a modulated train 

 as far as the level at which non-linear effects 

 occur is presented. The local breakdown observed 

 in the wave packet case is similar to that observed 

 in the breakdown of the modulated wave trains that 

 arise from natural random excitations. Secondary 

 breakdown does of course also occur on large enough 

 periodic waves, but modulation seems to cause this 

 phenomenon to take place at somewhat lower levels 

 of primary disturbance and in a slightly different 

 form. The artifically driven wave packet embodies 

 some of the most important features found in natu- 

 rally occurring waves, and since they can be gen- 

 erated in a controlled manner the effects can be 

 quantified. It is essential to understand this 

 process if one is going to make estimates of where 

 transition occurs on the basis of the amplitudes 

 of instability waves calculated from linear theory. 

 At present, most prediction methods rely solely on 

 the intensity of the most unstable wave. This is 

 clearly inadequate as breakdown is also dependent 

 on the modulation of the wave train, and consequently 

 the bandwidth of the amplified part of the spectrum 

 must also be taken into account in some way yet to 

 be established. 



Secondly, the transition from regular waves to 



turbulence appears to occur through a cascade pro- 

 cess. The stresses induced by a modulated wave 

 train cause steep shear layers to form in the bound- 

 ary layer. These support instabilities of higher 

 frequencies and shorter wavelengths than the waves 

 that caused the distortions, and these grow to large 

 amplitudes in appropriately shorter distances. This 

 process must at some stage be tempered by viscosity, 

 but in these experiments three levels of instability 

 have been so far detected. The lowest frequency 

 motion was artifically excited by the input pulse, 

 while the two successviely higher frequencies were 

 excited by random turbulence in the flow at the 

 particular location in space and time where local 

 instabilities existed. The development of a fine 

 scale structure is thus a local, almost explosive, 

 phenomenon. Such a cascade breakdown process pro- 

 vides the necessary mechanism for the generation of 

 fine scale motions that arise in a fully turbulent 

 flow. 



REFERENCE 



Gaster, M. , and I. Grant (1975). An Experimental 

 Investigation of the Formation and Development 

 of a Wave Packet in a Laminar Boundary Layer, 

 Proc. R. Soc. Land. A 347, 253-269. 



