decomposed into a set of individual free waves, with from one to five directional free 

 waves per frequency. The effects of the second order interactions are subtracted from 

 the measured record to determine the amplitudes and phases of the individual free 

 waves through an iterative procedure. This results in an expression for the potential 

 function and water surface that includes a full set of many free waves, and the corre- 

 sponding second order bound modes. The method succeeds in globally reproducing 

 the measured kinematics in the given deep water field records quite well, although 

 the largest errors are in the vicinity of the crest, where velocities are greatest, and 

 accuracy is most important. 



Another limitation of the Prislin and Zhang method is that the nonlinear interac- 

 tions are computed through the use of a Stokes-type perturbation expansion in wave 

 steepness. Based on experience with steady waves, a second order expansion of this 

 type is likely to be adequate in deep water, but if the method were to be applied 

 in transitional, and especially in shallow water, a much higher order representation 

 would be necessary (Fenton 1990). While it is theoretically possible to extend the 

 method in this manner, it would increase the magnitude of the computation substan- 

 tially, perhaps prohibitively. Representing an entire record in the global sense requires 

 many interacting free waves. Considering their interactions at high order would pro- 

 duce huge numbers of interacting terms that must be considered. An alternative, 

 local, approach would need to consider far fewer interacting waves. 



Other global methods rely on zero crossing analysis to identify particular waves 

 that are then analyzed by using steady wave theory for a wave of the same height and 

 period. This approach can provide an order of magnitude estimate for the kinematics, 

 but does not take into account the detail of the record, and thus can not be expected 

 to consistently provide better than order of magnitude accuracy. 



To include the detail of the record in wave by wave analysis. Dean (1965) adapted 

 his numerical stream function method to irregular waves, seeking a Fourier expansion 

 for the stream function that includes both cos j{kx — ut) and sinj(A;a: — tot) terms. 

 The method optimizes the Fourier amplitudes to best solve the free surface boundary 

 conditions at the measured water surface elevations from trough to following trough. 

 While this approach takes into account the detail of the record, the method includes 



