E. J. Richards, J. L. Willis, and D. J. M. Williams 283 
© WILLS (Water) 
© WILLIAMS 
002 +004 006 008 
™ 2 
SEie/aipu 
Fig. 15.5. Over-all rms pressures. 
smooth-flow over-all rms pressure level of 0.006q* obtained by Willmarth [3], 
while Williams [4] in his experiments at low supersonic speeds has pressure 
fluctuations at the walls which fall with forward Mach number but which are in 
general agreement with the low subsonic answers. If, as is more logical, the 
pressure fluctuations are plotted against the local skin friction at the walls, we 
get a level of 37, Tin the subsonic work, and a variation between 2.47, and 1.279 
in Williams' supersonic investigations; see Fig. 15.5. 
To evaluate the spectral content ofthese pressure fluctuations, it is necessary 
to bear in mind the purpose for which these spectra are to be used. If they are 
to be incorporated into structural-response calculations, the normal spectral 
measurement methods are satisfactory; if, however, it is necessary to calculate 
the radiated noise from the pressure fluctuations at the surface, it is usual to 
carry out the calculations in terms of turbulence being convected along the 
surface with some mean speed of flow of the turbulence. Thus, the significant 
spectra are those of turbulence as seen by an observer moving along the surface 
with the mean velocity of convection, not those at a stationary point. Such spectra 
* ais the mean flow in the dynamic head. 
t7ois the wall shearing stress or skin friction. 
