742 LAFOND [chap. 22 



surface, and all sound energy reaching the bottom was absorbed. This repre- 

 sentation was an ideal situation, but it approximated the natural sea-velocity 

 structure more closely than any previously considered. Even in this medium a 

 great deal of computation was required for the multiple refractions and reflec- 

 tions for each 0.1° ray. 



The computation of the acoustic energy refraction by internal waves is 

 shown in Fig. 13. The acoustic intensity of sound, as coinputed for each 10-ft 

 interval of range and each l-ft interval of depth, is shown by the shaded zones. 

 The sound intensity (dB reference level) is that corresponding to a ^ound level 

 of 60 dB at one foot from the directional source (depth 10 ft, distance ft) 

 along the horizontal. 



Above the thermocline the sound intensity decreased approximately as the 

 square of the distance from the source. Below the thermocline refraction 

 focused the sound rays as they passed through the internal wave into alter- 

 nately high- and low-intensity zones. The divergence and convergence of the 

 rays was directly related to the sinusoidal nature of the internal waves. 



In this problem, there was one high- and one low-intensity zone below the 

 thermocline for each interval of one wavelength. The width of the high- 

 intensity zones decreased with range, and the opposite was true for the low- 

 intensity zones. The variation with range was mainly caused by waves near the 

 source acting as a barrier to those at greater distance, i.e. progressively fewer 

 rays struck those waves increasingly distant from the source. 



The internal wave in the above problem caused horizontal changes in the 

 sound intensity of 22 dB over distances of less than one internal wavelength 

 (300 ft) at 400 to 700 ft in range. On the other hand, intensity changes in a 

 medium without the internal wave are about 5 dB within 300 ft at the same 

 range, and no intermittent zones of high and low intensity occur. Thus internal 

 waves play an important role in underwater sound transmission. 



g. Other related motions 



In the sea, internal waves appear to take the form of progressive waves. In 

 lakes and partially closed bodies of water, standing waves are found. The nature 

 of progressive waves between two liquids of different densities is described by 

 Lamb (1945). The theoretical water motions associated with this simple pro- 

 gressive wave are shown in Fig. 14. The fine arrows represent the streamlines of 

 particles. 



In the sea, in addition to the vertical oscillations, other evidence of this 

 circulation has been demonstrated. First, in the study of lateral shear motion, 

 direct observations of vertical dye streaks in the water become distorted by 

 the shear at the thermocline (Fig. 15). Secondly, other evidence of this motion 

 is shown by surface currents and other surface phenomena (LaFond, 1959a). 

 For example, in the Bay of Bengal, the surface showed long streaks of alter- 

 nately rough and smooth water. The ripples were 6 to 8 in. high and some 

 streaks extended to the horizon, varying in number from two or three to at 



