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Appendix A 

 Intersecting wave theory 



A.l Introduction 



The theory of multiple wave interactions presented by Ohyama, Jeng, and Hsu 

 (1995a) has been used for two purposes in this work. The most important function 

 was to suggest a form for a general three dimensional potential function representing 

 interacting waves. The form chosen is presented in Chapter 4. It also provided a 

 theoretical method for generating a complete, consistent set of records to use for the 

 development and testing of the LFI method. This appendix presents a review and 

 detailed critique of the intersecting wave theory. 



A. 2 Theoretical Background 



Ohyama et al.'s method is an extension of well accepted and verified methods. 

 It is essentially a Stokes type expansion in the wave steepness. As such, it is ex- 

 pected have greatest applicability in deep water. The flow is taken to be irrotational 

 and incompressible, and thus the governing equations are the same as those used in 

 chapter 4 and for most finite depth irrotational wave theory: 



• Mass conservation (Laplace equation) (Eq. 4.2) 



• Bottom boundary condition (Eq. 4.3) 



