E. J. Richards, J. L. Willis, and D. J. M. Williams 285 
can be obtained using space—time correlation methods; the curves of Fig. 15.6 
indicate typical results obtained by Willis and Bull in their work for various 
transducer spacings. The optimum convection speed can be obtained from the 
delay time giving the best correlation for the various spacings, or from the time 
delay for envelope tangency; the results differ very little. Figure 15.7 shows the 
convection speed based on different separations ofthe microphones. The variation 
of velocity so obtained is significant, indicating, as would be expected, that the 
large eddies in the boundary layer are convected at higher speeds than the 
smaller eddies. The convection speed of interest is clearly that of the noise- 
radiating eddies (i.e., the highest frequency at which the energy level is high). 
The fixed and moving frame spectra of pressure fluctuations can be obtained 
from the cross-correlation curves, the Fourier cosinetransform of the envelope 
to the fixed-point cross-correlation curves giving the moving-frame power 
spectra. Figure 15.8 indicates these two spectra and the essential differences 
between them also shown, but to an arbitrary scale, is the spectrum of the 
pressure—time derivative op/dt, a parameter directly related to the radiated 
noise from the wall pressure fluctuations [17]. 
In aviation, these pressure fluctuations are modified in many ways by the 
specific environment of the flow. For example, in separated flow over a narrow 
delta wing, Jones and Judd [5] have shownthat wing pressure fluctuations beneath 
the cast-off vortex are increased some tenfold and are well correlated over quite 
large areas of the wing. Thus, the noise radiated in such instances is presumably 
far greater than that calculated from normal turbulent boundary layers. Other, 
though smaller, increases occur, however, behind discontinuities in the surface 
or in regions of roughness, and these are presently being studied at Southampton 
[2]. For example, the variation of rms pressure behind a rectangular ridge of 
‘/,-in. length and 0.1-in. height in a boundary-layer flow is shown in Fig. 15.9. It 
is seen that the rms pressure increases with distance behind the ridge to a value 
r) 4 8 12 16 20 
7 
Fig. 15.7. Variation of convection velocity with distance along the 
tunnel wall. 
