Salve sen 



Rtl{wi-«+io)} 



Fig. 2 - Plot of the function 

 Fe I[iz^(x- s + iO)] 



For later reference we shall write the two terms in Eq. (23) as 



^(2)( 







^ 77U2 J 



ds f(s) Re I[ii^(x- s + iO)] , 



(24) 



7]( 2) (x) = l/(7j( 1))^ . 



We not turn to the numerical computation of the first-order and second- 

 order waves. A MAD computer program was prepared for this purpose. Be- 

 fore we discuss the final results of these computations, let us look at some of 

 the intermediate steps. It is interesting to note that the "pressure" function 

 f(s), defined by Eq. (21), is not sinusoidal far downstream but tends to the con- 

 stant value pgva'^/2, where a is the first-order wave amplitude, as can be seen 

 from Fig. 3. We also note (Fig. 4) that due to this constant "pressure" value 

 the first part of the second-order wave ■q^'^^i-x.) far downstream is sinusoidal 

 but with the mean line a distance va'^/2 below the undisturbed free -surface level. 

 The important fact is that this constant dislocation of the mean line is of exactly 

 the right magnitude to balance the constant part of the term -niVi")^) - ^iv'- ^■')^, 

 leaving only harmonic wave components far downstream. 



Plots of the final results, the surface elevation according to the first-order 

 and the second-order theory, are given in Fig. 5 for the case of 1.25-foot body 



Fig. 3 - Plot of the "pressure" 

 function f(x) 



604 



