106 



first order components are the largest components of the resulting wave field, and thus 

 give an approximation of the size of the resulting waves. This wave theory assumes 

 a zero Eulerian current. 



Standing Wave Figure 5.24 shows the results of the method for a standing wave 

 generated by two identical intersecting waves traveling in opposing directions. The 

 parameters of the waves are: Period = 10 sec, first order amplitudes = 3 m, prop- 

 agation directions, 15 and 195 degrees from the x axis, in deep water. The LFI 

 method to third order ( J = 3) finds the kinematics at the water surface almost ex- 

 actly. While these results show the complete wave, it is important to keep in mind 

 that as with all the previous results, each of the indicated points is in the center of 

 a separate window, and was computed independently of the other windows. In this 

 case, the standard window width was 1 sec, or one tenth the zero-crossing period of 

 the wave, with a third order potential function {J — 3), and four water surface nodes 

 distributed equidistantly in time in each window (M = 4), at each gauge, for a slight 

 overspecification, with 24 equations in 20 unknowns 



Short Crested Wave Figure 5.25 is the water surface at a point in time of the 

 short crested wave that would result in the reflection of a steady wave from a sea 

 wall, as indicated by figure 5.26. The parameters of the wave are: Period = 10 sec, 

 first order amplitudes = 3 m, propagation directions, 30 and 150 degrees from the x 

 axis, in deep water. Figure 5.27 shows the results of the method for this short crested 

 wave. The LFI method to third order again finds the kinematics for this wave almost 

 exactly. In this case, the standard window width was also 1 sec, or one tenth the 

 zero-crossing period of the wave, with a third order potential function ( J = 3) and 

 four water surface nodes (M = 4) in each window, for a slight overspecification, with 

 24 equations in 20 unknowns. 



Choice of Order 



As with the previous examples with steady waves, it is useful to examine a window 

 near the crest in order to determine the order necessary to accurately capture the 



