Chapter 33 

 OBSERVATIONS OF WAKE ECHOES 



ECHOES FROM WAKES, like those obtained from 

 other targets, vary considerably with the type of 

 sound gear employed, the prevailing oceanographic 

 conditions, and the physical constitution of the wake. 

 Before the observations are reviewed, it is necessary 

 to outline the theoretical concepts entering into the 

 reduction of the crude data obtained by measure- 

 ment. 



As regards the physical mechanism by which sound 

 is returned from a wake to an echo-ranging trans- 

 ducer, two limiting cases can be imagined. On one 

 hand, the multitude of microscopic scatterers may be 

 spread out so thinly that the phases of the scattered 

 sound waves are distributed at random — that is, so 

 that constructive and destructive interference are 

 equally probable. Then the average power returned 

 to the transducer is obtained by summing up the 

 contributions from the individual scatterers. On the 

 other hand, a wake might reflect sound specularly. 

 This alternative would occur only if the concentra- 

 tion of scatterers near the wake surface increased in- 

 wardly very rapidly. It is undecided as yet whether 

 or not specular reflection from wakes does occur; in- 

 conclusive evidence on this point will be discussed in 

 Chapter 34. In the present chapter, wake echoes will 

 be treated on the first assumption. Experience has 

 shown that this approach is usually quite satisfactory. 



33.1 CONCEPT OF WAKE STRENGTH 



33.1.1 Target Strength of a Wake 

 and Wake Strength 



Echoes from wakes differ in two important respects 

 from echoes from ships and other small targets. The 

 concept of target strength has been analyzed in Sec- 

 tion 19.1 where it was shown that for a target of finite 

 size the target strength becomes independent of range 

 at very long ranges and may be computed from the 

 equation 



T = E - S + 2H , (1) 



where E is the echo level in decibels above 1 dyne 

 per sq cm, S the source level or pressure level 1 yd 

 from the projector, in decibels above 1 dyne per sq 

 cm, and H the one-way transmission loss from the 

 source to the target in decibels. If equation (1) were 

 used to compute the target strength T^ for a wake 

 from the echo level at long ranges, Ty, would increase 

 with the range because, for practical purposes, the 

 wake extends infinitely in the horizontal direction; as 

 the range increases, more of the wake becomes ex- 

 posed to the sound beam, more scattering occurs, and 

 the target strength increases.. For the same reasons, 

 a transducer with a broad horizontal beam would 

 yield a higher echo level than a transducer with a 

 narrow pattern beaming sound at the same wake, 

 other things being equal. 



It is desirable, therefore, to introduce in place of 

 the target strength of a wake another characteristic, 

 which is essentially the target strength of a 1-yd 

 length of the wake. This quantity is principally a 

 function of the geometric dimensions and of the 

 physical properties of the wake alone and, therefore, 

 will be called wake strength and denoted by the sym- 

 bol W. The wake strength will here be defined in a 

 simple manner for an ideal wake, without regard to 

 the physical structure of actual wakes. In Section 

 33.1.2, an analysis of this wake strength in terms of 

 the physical constitution of the wake will be given, 

 including the effects originating from the finite length 

 of the sound pulses used in practice. 



The wake echo will now be treated as if it were the 

 echo from a plane strip having infinite horizontal ex- 

 tension (— oo< y <-j-oo) and a constant vertical 

 height h (depth of the wake) which is supposed to be 

 much smaller than the distance to the transducer. 

 The hypothetical strip is assumed to have a rough 

 surface, so that the reflection of sound by it is non- 

 specular and perfectly diffuse, with a dimensionless 

 coefficient of reflection s which is the fraction of sound 

 energy returned into a unit solid angle. The fraction 

 of sound energy reflected back, regardless of direc- 



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