amplitude function K(t) for large values of t. Indeed, the 

 short divergent waves in the vicinity of the track of the 

 ship, that is for small values of a, are associated with ti.c 

 value of the function K(t) for large values of t, as may be 

 seen from equations (23), (24a), (25a) and (12). Precise 

 knowledge of the asymptotic behavior of the function K(t) 

 as t -* °o therefore is critical. 



The behavior of the function K(t) as t -* «= has 

 been determined analytically in this study for the simple 

 case of the thin-ship and slender-ship approximations 

 Kw(t) and KqH) for an idealized ship bow form. More 

 precisely, the asymptotic behavior of the functions K^Ct) 

 and KQ(t) for the simple ship bow shape considered in this 

 study is specified by equations (45) and (67a, b). These 

 asymptotic approximations show that we have |Kn4(t)| = 

 (Xl/t^) and |K(,(t)| = (Xl/t^) as t - «>, They also show 

 that the Michell thin-ship approximation Kn^(t), which 

 corresponds to the thin-ship limit of the slender-ship 

 approximation K(,(t), is not uniformly valid in the limit t 

 -» <». It is possible to analytically determine the behavior 

 of the far-field wave-amplitude function K(t) associated 

 with the Neumann-Kelvin theory for an arbitrary ship 

 form, as is shown in [12]. Such an asymptotic 

 approximation for the function K(t) for large values of t 

 is useful because it provides an explicit analytical 

 relationship between the hull form and the Froude 

 number, on one hand, and the amplitude of the short 

 divergent waves in the vicinity of the track of the ship, on 

 the other hand. 



ACKNOWLEDGMENTS 

 This study was funded by the Office of Naval 

 Technology sponsored Exploratory Development Surface 

 Ship Wake Detection Project at the David W, Taylor 

 Naval Ship R&D Center. The authors wish to thank 

 Dr. Arthur Reed and Mr. Seth Hawkins for their interest 

 in the study and for their useful comments. 



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