Some preliminary measurements of the fluctuating pressure in a turbulent 

 boundary layer at the bottom of an open channel have been described by Einstein 

 and Li. [57] Willmarth [58] has reported some measurements of the fluctuating pres- 

 sure at the boundary of a pipe. He estimates that p = 3.5 x 10" 3 ( - pU 2 ), where U 



is the free-stream velocity, but the measurements may be in error because the fluctua- 

 tions may not be correlated over the entire area of the pressure-sensing device. Cer- 

 tainly, additional measurements are required to make possible an estimate of the space 

 correlation and the spectral density of the pressure fluctuations, as required by step 

 (1) above. 



Theoretical calculations of the boundary-layer noise have been attempted by 

 Ribner, [59] and more recently by Corcos and Liepmann, [60] and by Kraichnan, [61] 

 all using certain assumed characteristics of the pressure fluctuations in the layer. The 

 first two of these papers deal primarily with a boundary surface which is "floating" 

 i.e., unconstrained. Kraichnan, on the other hand, treats a square plate constrained at 

 its periphery; he also goes into greater detail concerning the character of the fluctua- 

 tions in the boundary layer. Which of these calculations is closer to the actual situation 

 cannot be determined until some measurements have been made of this form of noise. 



Other unsteady flows. — Before this section is concluded, mention should be 

 made of several other types of sound associated with unsteady flow which have received 

 some attention in recent years: 



( 1 ) "Jet-edge tones," which are generated when a jet impinges on a thin plate 

 or wedge. The sound contains a predominant frequency determined by a periodic 

 undulation of the jet, the frequency depending primarily on the velocity of the jet 

 and the separation between the mouth of the jet and the edge. Richardson [39, 62] 

 has described his own and several other investigations of the phenomenon. Other dis- 

 cussions have been published by Curie, [63] by Powell, [64] and by Bouyoucos and 

 Nyborg. [65] Two alternative mechanisms have been suggested. Richardson and Curie 

 believe the undulations are caused by instability of the flow itself, whereas the others 

 believe that the sound reacts on the jet and "triggers" the instability. In either case, 

 the sound is presumably generated by a fluctuating lift force on the edge. 



(2) "Orifice-pipe tones," generated when a fluid discharges through a sharp- 

 edged orifice at the end of a tube. The frequency of the sound has been determined 

 for a wide range of conditions by Anderson. [66] The sound, in this case, is probably 

 a simple source associated with periodic fluctuation in the rate of efflux from the 

 orifice. 



(3) Resonant cavities excited by external flow past the mouth of the cavity. 

 The frequency of these sounds has been investigated by Blokhintzev [67] and by 

 Harrington. [68] There seems to be some interaction between the cavity and the un- 

 steady flow past the mouth, because the predominant frequency of the sound may 

 differ somewhat from the frequency at which the cavity resonates in the absence of 

 flow. The sound can be considered to be a simple source associated with alternating 

 flow in the mouth of the cavity. 



The investigations of jet-edge tones, orifice tones, and resonant cavities have 

 been concerned primarily with the frequency of the sounds, without any attempt to 

 determine their amplitudes. Accordingly, it is not possible to say whether any of them 

 are significant sources of underwater noise. However, the uncertainty results from the 

 lack of adequate descriptions of these flows. Once suitable descriptions of the flows 

 become available, the associated sound pressure can be calculated by the methods 

 described in this section. 



REFERENCES 



1. R. G. Folsom, E. D. Howe, and M. P. O'Brien, "Hydraulic Noise." Univ. of Calif., 

 OSRD 949, June 1942. 



273 



