Calculation of the effect of internal waves on oceanic 

 sound transmission 



Stanley M. Flatt6 



Universily of California. Santa Cruz. California 95064 



Frederick D. Tappert 



Courant Institute of Mathematical Sciences, New York University. New York, New York 10012 

 (Received 22 August 1975) 



The signal received by a hydrophone in the ocean many kilometers from a steady sound source fluctuates 

 dramatically due to variations of the speed of sound in sea water. By inserting an empirical model of 

 intemal-wave-generated sound-speed variations into an acoustic-transmission computer code, we have 

 shown that internal waves cause significant vanations in sound transmission at 100 Hz. comparable in size 

 and frequency to the vanations observed m field experiments. We have also studied the usefulness of 

 vertical hydrophone arrays. 



Subject Classification: 30.25, 30.82; 28.60. 



INTRODUCTION 



Acoustic transmission in the ocean is profoundly af- 

 fected by the dependence of the speed of sound on ocean- 

 ic depth, range, and time. The speed of sound, in turn, 

 is determined by oceanographic quantities: pressure, 

 temperature, and to a lesser extent, salinity. 



In a typical 4-km-deep ocean, the sound speed c has 

 a minimum as a function of depth z at about 1 km, with 

 a value close to 1500 m/sec. Values of c at the surface 

 and bottom are a few percent higher than at the mini- 

 mum. From an oceanographic point of view the mini- 

 mum is due to the competition between the drop in tem- 

 perature and the rise in pressure as one descends in 

 the ocean. The minimum causes sound to be refrac- 

 tively contained in the volume of the ocean, resulting 

 in a "sound channel, " and making possible sound trans- 

 mission over thousands of kilometers at frequencies 

 below 1 kHz.' (Higher frequencies are absorbed.) 



The sound-speed profile c{z) varies with geographic 

 position. For ex.imple, the sound channel minimum 

 rises as one moves toward colder Northern waters. In 

 addition, the depth of the ocean changes due to the to- 

 pography of the bottom of the sea. Hence any acoustic 

 transmission experiment over hundreds of kilometers 

 or more will be subject to a range-dependent sound- 

 speed profile. A great deal of work has gone into map- 

 ping the expected differences in transmission due to 

 differences in geographical location.^ 



The strongest time variation of c(^) occurs as a re- 

 sult of seasonal changes in temperature. These long- 

 term time variations have also received considerable 

 attention, although in principle the changes between 

 winter and summer are no more difficult to deal with 

 than a significant change in geographical position. 



Any experimenter who has done a long-range acoustic 

 transmission experiment can attest to the fact that con- 

 siderable (5-30-dB) variations in signal are observed 

 over periods ranging from a few minutes to several 

 days, with several hours being typical.^ When surface 

 interactions are absent or have been filtered out, and 



for fixed source and receiver, these fluctuations must 

 be caused by variations in the sound-speed field through 

 which the sound passes, and the sound-speed variations 

 must have an oceanographic origin. Yet until now al- 

 most no quantitative connection has been made between 

 these "rapid" acoustic variations and any realistic 

 oceanographic phenomenon. Over the years, however, 

 there has been much speculation and order-of-magni- 

 tude correlation with internal-wave motions.^ 



The ocean contains a random field of internal waves, 

 with periods ranging from j to 24 h. The intensity of 

 these waves has been estimated from measurements of 

 temperature and current fluctuations in the ocean, and 

 the associated effect on sound speed has been calcu- 

 lated. ^'^ The root-mean-square sound-speed fluctua- 

 tions due to internal waves is at a level of 10'', two 

 orders of magnitude below the variation which causes 

 the sound channel.^ 



In this paper we demonstrate that the internal wave- 

 field in the ocean causes significant fluctuations in 

 long-range acoustic signals, comparable in size and 

 period to those observed in field experiments. Our 

 method of calculation involves a computer code (devel- 

 oped by us) which propagates CW acoustic signals 

 through a sound-speed field that depends on both depth 

 and range. The code calculates the random part of the 

 sound-speed field from an internal-wave spectrum, 

 and simulates the time variation by stepping the inter- 

 nal wavefield in time, and propagating the acoustic 

 signal at each time. ' We have used a frequency of 100 

 Hz. 



In this paper we also demonstrate the usefulness of 

 a vertical array of hydrophones in reducing intensity 

 fluctuations in long-range acoustic transmission. 



Other work relating acoustic fluctuations to internal 

 waves has been in progress simultaneously with ours. 

 DeFarrari considered only one internal wave, the in- 

 ternal tide, rather than a full spectrum. ° Porter et al. 

 considered a full spectrum of internal waves, but used 

 a thin-layer model for internal waves as they affect 



201 



