PART IV: EXAMPLE CALCULATIONS 



General Comments 



71. Two examples are presented. These hypothetical situations demon- 

 strate applications of the shoreline model with an operative seawall boundary 

 condition and allow checking of user implementations of the programs given in 

 Appendix A. An attempt was made to give semi-plausible examples while also 

 preserving clarity. This resulted in two idealized cases for which most of 

 the common structures and boundary conditions could be included. The first 

 example is that of an initially straight shoreline bounded on one side by a 

 jetty. The beach is protected by the combination of a detached breakwater and 

 a straight seawall segment. The second example is a curved pocket beach lying 

 between two headlands and protected by a curved seawall. Hanson and Kraus 

 (1985) show results of several other sample calculations. 



72. In the examples, the wave field is introduced artificially; the 

 breaking wave height and breaking wave angle were fabricated "by hand" to 

 achieve the desired trends in shoreline movement in order to exercise the sea- 

 wall constraint algorithms. The breaking wave data are set in the subprogram 

 INDATA which is given in Appendix A. Values of the time and space steps and 

 other parameters are entered via FORTRAN DATA statements. The names of param- 

 eters and variables closely follow the notation of the main text of this re- 

 port. The important exceptions are: the angle "theta," denoted as "Z," and 

 the empirical coefficient "K," denoted as "K1" in the program. 



73. Both examples can be run using either the explicit or the implicit 

 numerical scheme, programs YSEXP and YSIMP, respectively, in Appendix A. In 

 the latter part of these programs a calculation is made to check sand volume 

 conservation. It can be verified that volume is conserved to within trunca- 

 tion error. 



Stability 



74. Before proceeding to the examples, the stability properties of 

 the shoreline model are briefly reviewed. It can be shown (e.g., Hanson and 

 Kraus 1 980 ; Kraus and Harikai 1983) that for small breaking wave angles and 

 constant wave height, Equation 1, together with Equation 2, reduces to the 

 functional form of the heat equation, the governing equation derived by 

 Pelnard-Considere (1954). The accuracy and stability properties of numerical 



31 



