Computation of the Motion of Long Water Waves 



SOLITARY OR 

 OSCILLATORY 

 WAVE IN 

 + X-OIRECTION 



(shallow water eqnsl 

 EXPLICIT 



IMPLICIT IN 

 X-DIRECTION 



IMPLICIT IN 

 Y-DIRECTION 



EXPLICIT 

 (uses advanced 

 velocities, however) 



T = TOP;STOP 



Fig. 2. APPSIM2 flow chart 



The deep and shallow portions are connected smoothly by a cosine 

 curve. 



For the solitary wave simulation, the pertinent parameters 

 were L, = 38, L2= 13, x^. = 14.5, Xg = 19.5, y^. = 7,75, yg = 2,75, 

 A = 0.25, At = 0.2165, and 110= 0,1, The wave was started with its 

 crest lying along Xq = 8.0 and propagated in the positive x-direction 

 toward the shelf. Chan and Street [ 1970a] showed that the effective 

 half-length of a solitary wave of amplitude t]q = 0.1 is about 11 so 

 it is necessary to correct the initial Boussinesq [ Wiegel, 1964] 

 wave profile for the influence of the wall at x = 0; however, it was 

 unnecessary to correct the leading portion of the wave for the bottom 

 influence. The initial u-velocity distribution was calculated from 

 Eq. (6) under the assumptions that v= 0, t| = r|(x,t) and the wave is 

 moving at a constant speed Co = 1 + 0.5 t|o [Wiegel, 1964] with 

 constant form. In addition At was selected in accordance with the 

 Courant-type condition 



At< A 

 ^0 



Results of the solitary wave computation are shown in Figs. 3-5. 



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