The Physical Processes Causing 

 Breakdown to Turbulence 



M. Gaster 



National Maritime Institute 



Teddington, England 



I want to present some recent experimental observa- 

 tions that provide further insight into the physical 

 processes that occur in the transition from a lami- 

 nar to a turbulent boundary layer. We know that 

 external disturbances, such as free-stream turbu- 

 lence and sound, excite small pertubations in the 

 laminar flow, and that under certain conditions 

 these may develop downstream in the form of growing 

 wave trains. At low pertubation levels these un- 

 stable travelling waves are adequately described 

 by the linearised equations of motion. Measure- 

 ments on weak artificially excited waves have, by 

 and large, provided excellent confirmation of linear 

 theory. Far downstream the amplitudes of the per- 

 tubation velocities will, however, become too large 

 for the neglect of the non-linear terms to be valid, 

 and a non-linear description of the motion is nec- 

 essary. Even in the relatively simple situation 

 of the constrained parallel Poiseuille flow, which 

 has been extensively studied, the non-linear the- 

 ories so far developed can only weakly describe 

 non-linear events, and even then the computations 

 are very involved. These non-linear theoretical 

 models are nevertheless very helpful in describing 

 the various interactions between the fundamental, 

 its harmonics, and the mean flow, but they cannot 

 go far toward providing a model of the process of 

 breakdown to turbulence , nor are they intended for 

 that purposes . 



Non-linear analyses have been concerned mostly 

 with the evolution of purely periodic wave trains. 

 In the case of linear problems it is quite proper 

 to consider any disturbance in terms of its Fourier 

 elements. Knowledge of the behaviour of purely 

 periodic wave trains enables more complex distur- 

 bances to be described. Unfortunately this is not 

 the case when the disturbance is non-linear, and 

 the welcome simplification obtained by breaking down 

 a problem into harmonics is no longer valid. When 

 the initial disturbances arise from natural rather 

 random stimuli the linear wave train will initially 

 consist of a band of unstable waves. After some 



amplification a slowly modulated almost sinusoidal 

 oscillation will inevitably develop. When the 

 selective amplification is very large, as is the 

 case in many boundary layer flows, the modulations 

 are slow, and it does not seem too much of an 

 idealisation to treat the non-linear problems 

 analytically as if it were a purely regular wave 

 train. It turns out, however, that the degree of 

 modulation does not have to be large for its in- 

 fluence on the Reynolds stresses and thus the 'mean 

 motion' to be very significant. In a typical ex- 

 periment on a laminar boundary layer over a flat 

 plate in a low turbulence wind tunnel one finds 

 that the instability waves are modulated suffi- 

 ciently to influence the transition process. It 

 is found, for example, that breakdown to turbulence 

 occurs violently and in a random manner quite un- 

 like the type of breakdown that is observed in 

 controlled periodic wave trains. Measurements on 

 isolated wave packets also show the effect that 

 modulation of the wave train has on transition, but 

 in a more controlled way. 



Previously reported measurements [Gaster and 

 Grand (1975) ] on artifically excited wave packets 

 showed consistent and quite well defined deviations 

 from the structure predicted by linear theory. 

 Since the maximum level of the velocity fluctua- 

 tions measured lay below that for which significant 

 non-linearity is exhibited by regular periodic wave 

 trains , the reason for this behaviour was at that 

 time unclear. In the experiments only one level 

 of input excitation was used and so there was no 

 direct way of assessing the importance of the non- 

 linear terms. These experiments have been repeated 

 at the National Maritime Institute with various 

 levels of input excitation and it has now been con- 

 clusively established that the previously observed 

 warping of wave fronts and the non-Gaussian char- 

 acter of some of the hot-wire signal envelopes arose 

 from non-linearity. This behaviour can best be il- 

 lustrated by showing a comparison of the hot-wire 

 signals that arise: (a) with a sinusoidal input. 



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