PART II: REGIONAL COASTAL PROCESSES WAVE PROPAGATION MODEL (RCPWAVE) 

 Background Information 



5. Linear wave theory was chosen as the initial level of sophistication 

 for the short-wave modeling component because, historically, it has been shown 

 to yield fairly accurate first order solutions to wave propagation problems. 

 Considering both accuracy and cost, it is currently the most feasible way to 

 model waves on a regional scale. Modeling short-wave processes using either a 

 fully two-dimensional nonlinear wave theory or a two-dimensional spectral re- 

 presentation of irregular waves is presently impractical for the types of ap- 

 plications anticipated for this modeling system. 



6. Much of the early work addressing the problem of linear, monochro- 

 matic wave propagation was based on wave ray methods and the manual construc- 

 tion of refraction diagrams (see Johnson, O'Brien, and Issacs ( 1 948) ; Dunham 

 (1951); and Pierson, Neumann, and James (1952) for examples). During the 

 1960's and early 1970's the refraction problem was solved in a more efficient 

 way through the use of the computer (for examples see Harrison and Wilson 

 (1964), Dobson (1967), Noda et al. (1974), and Rabe (1975). Refraction theory 

 fails in regions of complex bathymetry where waves are strongly convergent or 

 divergent. Crossing wave rays results in the computation of erroneously large 

 wave height estimates. Strongly divergent wave fields manifest themselves in 

 regions of unusually small wave heights. Laboratory and prototype observa- 

 tions show that refraction theory is inadequate under these conditions (Whalin 

 1971 and 1972). 



7. Inclusion of diffractive effects into the equations governing wave 

 propagation allows wave energy to be diffused from regions of convergence to 

 regions of divergence. Berkhoff (1972 and 1976) derived an elliptic equation 

 approximating the complete wave transformation process for linear waves over 

 an arbitrary bathymetry constrained only to have mild bottom slopes (hence the 

 designation "mild slope equation" (Smith and Sprinks 1975)). The mild slope 

 equation can be expressed in the form 



(<* rO+M cc f*)^ 2 ^* = o d) 



\ g 3x/ 3yV g 3y/ c 



