23 



and (b) a pulsed input. As in the previous series 

 of experiments the boundary layer flow was excited 

 by an acoustic device mounted in a recess on the 

 reverse side of the flat plate. A small hole 

 through the plate provided the necessary fluid 

 dynamic coupling at a point on the boundary of the 

 working face. Figure 1 shows a set of hot-wire 

 anemometer records taken with the probe mounted 

 just outside the boundary layer one metre down- 

 stream of the leading edge. The exciter was driven 

 sinusoidally at four different amplitude levels 

 increasing from (i) to (iv) . The velocity fluc- 

 tuations appear to be regular and show no harmonic 

 or other distortion until the level of turbulence 

 intensity exceeded 1% peak-to-peak of the free- 

 stream velocity (see iv) . Exciting the flow with 

 isolated pulses on other hand, produces a some- 

 what different picture. Figure 2 again contains 

 four hot-wire records obtained with different 

 levels of drive applied impulsively. At the lowest 

 level shown the signal consists of a smooth roughly 

 Gaussian packet of ripples, but even a small in- 

 crease in driving amplitude produces a clearly 

 discernible distortion to this signal. These dis- 

 tortions are similar to those obtained in the 

 earlier experiments quoted. As the amplitude is 

 further increased the signal becomes increasingly 

 distorted until at some level a secondary burst 

 of relatively high frequency oscillations appears. 

 It should be remarked that the amplitude scaling 

 on both Figures 1 and 2 are identical, showing that 

 non-linear effects occur at much lower amplitudes 

 for the impulsively applied disturbance than for 

 a periodic one. In these particular experiments it 

 appears that non-linearity becomes apparent in the 

 hot-wire signal at a peak to peak amplitude of only 

 1/5^ that for a continuous wave train. 



The high frequency oscillation appears to be 

 associated with a steep shear layer that forms 

 within the velocity profile momentarily as the 

 wave packets sweep past the measuring station. 

 These shear layers initially appear on either side 

 of the centre line, and not surprisingly therefore 

 the peak levels of the high frequency secondary 

 oscillation also arise off centre at roughly these 

 locations. The high frequency waves grow rapidly 

 with downstream distance, initially developing 

 exponentially but later the growth levels off. At 

 that stage the filtered secondary wave packets were 

 observed to distort in a way reminiscent of the 



FIGURE 2. Hot-wire signals from pulsed excitation. 



primary wave packet. It was therefore conjectured 

 that there might be yet a further level of insta- 

 bility on the secondary wave oscillations when 

 these became sufficiently large. Just two days 

 before leaving for this meeting this idea was 

 tested. Hot-wire signals from appropriate regions 

 of the flow were filtered to see whether there was 

 any signal above the frequency of the secondary 

 oscillations. When the secondary wave amplitude 

 was large, a burst of high frequency oscillations 

 could be seen on the oscilloscope. Figure 3 shows 

 the result of applying a high-pass filter, set to 

 pass above 2 kHz, to such a hot-wire anemometer 

 signal. The time scale of this record is con- 

 siderably expanded compared with that of Figures 1 

 and 2, and shows that the oscillation frequency in 

 the burst was around 5 kHz. The basic primary 

 wave packet of roughly 150 Hz developed over 1 m 

 before breaking and supporting a secondary burst 

 of 1 kHz. This secondary instability grew in am- 

 plitude to levels large enough to indicate the in- 

 fluence of non-linearities in a distance of roughly 

 4 cm. The tertiary mode of 5 kHz detected at this 

 stage seems likely to grow even more rapidly. One 

 can only presume that further stages in this evo- 

 lutionary process are inhibited by viscosity. 



These experiments on the non-linear wave packet 

 and its breakdown to turbulence are as yet incom- 

 plete and it is my purpose here to indicate only the 



FIGURE I. Hot-wire signals from sinusoidal excitation. 



FIGURE 3. High frequency burst. 



