Computation of the Motion of Long Water Waves 



"^^ (t?) 







for 



[" l + cos (iTx/xd) 



for 



< X < Xd 



X > X, 



(53) 



is applied to the free surface. Here p^ is the amplitude of the 

 pressure pulse, Tp is its period and x^j is the horizontal length of 

 the surface subject to the prescribed pressure. Equation (53) was 

 employed by Fangmeier [ 1967] in solving the same type of problems 

 using time-dependent potential flow equations. 



In the first case, a channel of the length L| = 30.0 was used. 

 The computation domain consists of 80 X 24 cells, each with 6x = 

 0.30 and 6y = 0.iO. We used po=0.iO, Tp=7.6 and xd=4.0 in 

 Eq, (53) to generate the surface disturbances. The development of 

 the u field is shown in Fig. 10. The plot increment is 0.0 25 per 

 contour line with u = 0,0125 on the contours closest to the ends of 

 the channel. At t = 10,0 the leading wave leaves the generating 

 area and progresses to the right. At t = 43.493 the first wave runs 

 up the right-hand wall and reflection begins to interfere with the on- 

 coming waves. As a result, a standing wave pattern occurs when 

 t = 72.986 to t = 84. 233. 



T ■ T8.734 



7*82.484 



T' 84.233 



Fig. 10. Periodic waves (u contours) 



179 



