286 Lecture 15 
twice that of the smooth-flow condition and ceases to have an effect some 20 
heights downstream. Further studies of the detailed effects of discontinuities, 
roughness, pressure zradients, and waviness of surface are proceeding at 
Southampton and will be reported later. The work is clearly of great interest in 
a wide variety of contexts as will be shown later by an elementary attempt to 
illustrate the significance of these results. 
15.2.1. The Radiated Sound from a Small Flat Plate 
It is difficult to check the theory of radiated noise from these pressure 
fluctuations since it is impossible to place a microphone, shielded from the flow, 
Fig. 15.8. Comparison of spectra of pressure 
fluctuation on the wall adjacent to a turbulent 
boundary layer. Curves: (1) fixedaxis, (2) moving 
axis, (3) moving axis + 6 db/octave (arbitrary 
ordinate scale), 
within the restricted space of a wind-tunnel working section and also in the far 
field in which reactive effects are absent. Some attempts, however, have been 
made at Southampton to obtain the radiation from flat plates in jet flows. The 
agreement between the measured and predicted far-field noise [6], which is quite 
good, justifies the use of existing theory in the prediction of radiated noise from 
a boundary layer. The only reference necessary atthis point is to the directional 
pattern to be obtained. Figure 15.10 shows a plot of the noise variation circum- 
ferentially around a small aerofoil placed at zero incidence in a jet compared 
with the theoretical pattern obtained from a single dipole with its axis at right 
angles to the surface. Since the noise radiated along the surface is theoretically 
zero for this type of wall pressure radiation, we cannot obtain any true indica- 
tion of the noise radiated along the surface without introducing theories of scatter 
and diffraction. With present knowledge, therefore, the best method of calculating 
