III-118 



terms for m ^ 3 can be ignored. This appears to be somewhat doubtful, and 

 Marsh offers no substantiating arguments . For frequencies and wave heights of 

 interest, a is often larger than one. Furthermore, nothing is mentioned about 

 the behavior of the fni('^ > M-)- Since these involve inverse transforms of the 

 function describing the sea surface, they may have large values for certain \ 

 and u . In summary, we cannot rely on the bounded or decaying nature of the 

 ^mO^ ' U ) or small values of a to assure the legitimacy of truncating the series 

 after the first three terms . 



(4) In the reduction of certain integrals, it is assumed that 



a = (ksV2q) = (0-0564)(fj^^)(s^^^^f (III-163) 



is "large." Marsh's analysis, as presented, does, not indicate how large this 

 should be . He does assume later that a^ is large relative to a (an order of 

 magnitude of more). For one kilocycle sound, we need a wind speed of 15 knots 

 or more for this to be so. This in turn requires o to be larger than one, making 

 assumption (3) questionable . 



(5) The mean square surface height, h^ , is related to the wind speed 



by 



(h f = 2.42 - 10^ (s, ^ f (III- 164) 



^ feet knots 



and the average trough to crest wave height, H, is related to h by 



H = 1.77h (III- 165) 



Marsh applies the foregoing analysis to the case of a wave field which 

 can be viewed as the composition of a finite number of rays with substantially 

 plane wave fronts which impinge on the surface and undergo scattering. The 

 medium is assumed to be an isothermal surface layer of depth L . The limiting 

 ray for a surface source and receiver is denoted by Pq, with Fj denoting the other 

 rays which are reflected from the surface . The diagram below illustrates the 

 situation. 



FIGURE III-43 SKETCH OF LIMITING SOUND RAY BENDING 



artbur Sl.lLittleJnt. 



S-7001-0307 



