DECAY OF WAKES 



539 



larger bubbles, which would persist longer at great 

 depths. More complete measurements would be re- 

 quired on submarine wakes of different depths before 

 any detailed conclusions can be drawn as to the varia- 

 tion of wake strength with depth. 



34.3.3 



Model Propellers 



The studies of echoes from wakes of model pro- 

 pellers, reported in Section 33.5, are not sufficiently 

 detailed to compare with theoretical predictions. 

 While echo levels were quantitatively determined, 

 neither the geometry of the experiment nor the trans- 

 ducer and hydrophone directivities are well enough 

 known to make possible a prediction of the echo 

 levels from the known properties of air bubbles. These 

 measurements are of theoretical interest, however, 

 because they provide information on the change of 

 wake echoes mth depth. This information has al- 

 ready been discussed before. 



The data also provide an interesting qualitative 

 confirmation of scattering theory. As is evident from 

 Figures 9 and 10 of Chapter 33, the echo level re- 

 mains relatively constant in the first 30 ft of increas- 

 ing depth. In this same depth interval the attenua- 

 tion in the wake, shown by Figures 3 and 4 of Chap- 

 ter 32, decreases from a high value near the surface 

 to less than 5 db at 30 ft. This behavior is in accord 

 with equation (3) ; this equation predicts that as long 

 as the transmission loss is more than a few decibels, 

 the amount of sound scattered from a collection of air 

 bubbles in water will be independent of the density 

 of bubbles in the water. 



34.4 



DECAY OF WAKES 



The observations on the decay rate of a wake's 

 acoustic properties should be consistent with the rate 

 of disappearance of bubbles, if bubbles are actually 

 responsible for scattering and attenuation of sound 

 by wakes. Although optical measurements of the 

 bubble density concentration in wakes have been 

 contemplated, at present there are not available any 

 nonacoustic observations of the rate of decay of 

 bubbles. Neither does physical theory permit pre- 

 dicting the rate of wake decay. As set forth in Section 

 27.2, the turbulent internal motion may be the factor 

 which determines the "life-time" of wakes. However, 

 an adequate theoretical analysis of the effect of tur- 

 bulence on the rate of rise of bubbles in wakes is 

 still lacking. 



Pending the solution of this fundamental problem, 

 the equations (49) and (50) of Chapter 33 suggest a 

 partial test of the theory of decay of acoustic wakes. 

 These equations established a quantitative relation 

 between the decay rate of the wake strength and that 

 of the total transmission loss across the wake; more- 

 over, they do not involve any quantities which are 

 unknown or difficult to determine. With this test in 

 mind, simultaneous observations of the decay rates 

 dHy./dt and dW/dt were made for a number of wakes 

 laid by the E. W. Scripps, on November 28, 1944; 

 these experiments have already been described, and 

 the results were summarized in Table 2 of Chapter 32 

 and Table 9 of Chapter 33. The results, though in- 

 sufficient to verify the relationship predicted theo- 

 retically, do not seem to be inconsistent with it. 



According to the discussion in Section 33.1.4, the 

 following relation should hold for short pulses and 

 fresh wakes: 



dW _ r o.46e-°'^^"'^°^"' "I ro dH,. n dH^ 



dt Ll-e-'''""'"H«; dt ~w dt ■ ^^^' 



The factor F in brackets can be read from Figure 4 in 

 Chapter 33, using HwTa/w as argument; rg was equal 

 to 2.4 yd, as 3-msec signals were used. The width of 

 the Scripps wake is 45 yd at the age of 5 minutes; 

 hence ro/w is about 0.05. The results of the numerical 

 test of equation (10) are presented in Table 7. The 

 observed and computed ratios {dW/dt)/{dHy,/dt) 



Table 7. Observed and predicted decay rates. 



seem to agree as to order of magnitude. Little more 

 can be expected, considering the high sensitivity of 

 the test following from the rapid variation of the 

 function F with H„. 



