(1978). This filter removes cell-to-cell oscillations introduced as a result 

 of the differencing scheme used to compute the new wave numbers. Row-by-row 

 marching proceeds until solutions are computed along row i=2. 



29. Lateral boundary conditions for a row are specified at the conclu- 

 sion of calculations for that row. The value of all variables at cells j=N 

 and j=1 are set equal to their values at cells j=N-1 and j=2 , respec- 

 tively. This boundary condition implies that the change in the variable in 

 the y-direction is zero. The condition is most valid when the bathymetric 

 contours are nearly straight and parallel to the y-axis. For this reason it 

 is recommended that users orient their grid system so that the y-axis is 

 nearly parallel to bottom contours along the lateral boundaries. 



30. Boundary conditions along the seaward extent of the grid are used 

 to initiate the shoreward marching algorithm. They are computed from deep- 

 water wave input supplied by the user along with the following assumption. 

 Bottom contours extending from the offshore grid row i=M out to deep water 

 are assumed to be straight and parallel to a line making an angle of 9 with 

 the y-axis. In other words, Snell's law is assumed to be valid from deep 

 water to the outer boundary of the grid system. No inshore boundary condi- 

 tions (along row i=1) are required because of the foreward marching solution 

 scheme. 



Wave Transformation Inside the Surf Zone 



Theoretical basis 



31. Waves approaching the very nearshore zone tend to steepen and even- 

 tually break because of decreasing water depths. Shoreward of this breaking 

 point dissipative energy losses due to turbulence strongly influence the wave 

 height. Linear theory does not allow for prediction of the breaker location 

 nor for wave transformation across the surf zone. Instead, empirical and ap- 

 proximate methods must be used to describe the breaking process. 



32. The first aspect to consider in surf zone transformation of waves 

 is incipient wave breaking. Iwata and Sawaragi (1982) reviewed many criteria 

 for determining wave characteristics at the breaking point. One which is ap- 

 pealing because of its basis on wave physics defines breaking as the point 

 when the particle velocity at the wave crest exceeds the wave celerity. The 

 following formulas: 



18 



