E. J. Skudrzyk and G. P. Haddle 263 
shaped hydrophone can then be expected to have a flow-noise response propor - 
tional to 
Fi =? ae 
(@) Rll ( ) 
The power-spectrum decrease will be proportional to the fourth power of the fre- 
quency and to the square of the product of the linear dimensions of the hydrophone. 
A circular hydrophone, as a first approximation, may be resolved into a 
central strip and a number of shaded strips, n-1~n, the strips being all ofa 
width equal to the transverse correlation distance. The resulting force on the 
receiver, then, is given approximately by 
odes an gg aye LP. A a SL faire 
p=18,+4@-y24 nos +[75| \Z _ (00.4: ets (24) 
If the width of the receiver is much greater than the correlation length, the 
second term predominates as long as the frequency is not too high. The cir- 
cular hydrophone can therefore be expected to behave like a perfectly shaped 
hydrophone at the high, but not at the very high, frequencies. At very high fre- 
quencies, the flow-noise sensitivity of the circular hydrophone will probably 
increase again. 
A rectangular hydrophone is particularly sensitive to flow noise. The flow- 
noise sensitivity of a hydrophone can be considerably reduced (as long as the 
nearfield pressure determines the received level) by varying its width from a 
small value to a maximum in the middle and to a small value again at its end. 
In a hydrophone of this shape, the pressure maxima and minima of the noise 
pressure (Fourier components of the noise pressure) cancel one another to a 
higher degree as they are transported by the flow across the hydrophone area. 
The effect of varying the width of the hydrophone is similar to the shading of 
arrays of hydrophones. Its response outside the main maxima-—that is, for the 
higher frequencies of the turbulence—decreases considerably. Because of the 
approximate isotropy of the eddies, the flow-noise sensitivity of a perfectly 
shaped hydrophone can be expected to be reduced by a factor of 
_ | sin(kl;/2) 7 
=| Ky11/2 | 2) 
Figure 14.3 shows a graphical representation of the square of this factor, which 
determines the received power spectrum, for a hydrophone that has a diameter 
4.3 times the boundary-layer thickness. This curve is very nearly the same as 
the curve determined for the hydrophone sensitivity from Willmarth's [11] 
measurements. The range of these measurements, however, extends over only 
1.5 decades (energy levels); therefore, this apparent agreement does not mean 
too much. However, the theoretical curve explains the steep slope over the range 
0.5 <27f5*/Up < 0.8 that has been observed by Willmarth and Harrison and that 
has not been observed at frequencies greater than those of the buoyant-unit runs 
to be described later. Doubling the linear dimensions now reduces the flow-noise 
level by 12 db, and doubling the frequency reduces the spectral level by 12 db. 
