Stveetj Chan and Fromm 



The evolution of the free surface is illustrated by free sur- 

 face maps in Fig, 3, while Fig. 4 shows a v- velocity map for 

 t = 19.5. The maps are printed during program execution by a sub- 

 routine that scales the variable values on a range running from a 

 minimum of zero to a maximum of ten. Only odd numbers are 

 printed at their corresponding node points. These maps are ex- 

 tremely useful for initial interpretation of the data. Later, quanti- 

 tative studies of results can be made because the u, v, r\ fields 

 are stored on tape after every five time steps and maps are made 

 after every 20 to 40 steps. Thus Fig, 5 illustrates a quantitative 

 comparison between the two-dimensional results and the three- 

 dimensional simulation at t = 19»5 for y = and y = 1^2* Both 

 the effect of wave refraction and the nonlinear response of the flow 

 are evident. 



As another example. Fig, 6 contains pictures of the develop- 

 ment of the Ti, u, and v fields for oscillatory waves shoaling on a 

 shelf. The pertinent parameters were I_| = 66, 1-2= ^1 , x-p= 25,5, 

 Xg=45.5, y^= 25.5, y3= 15.5, A =0.5, At = 0.5, and 2r|o = Hq = 

 0.05. The input wave at Wall i (Fig. 1) had assumed length L<, = 20 

 and speed Cq = 1,0 so the period Tq = 20, The actual computed 

 length was essentially 20 also. In this case we sought to simulate a 

 large region so A was large; even so 458K bytes of core storage 

 were required for the program. In spite of the rather coarse grid 

 the computed properties of the waves were smooth and well behaved. 



T = 44.5 



T= 68.5 



U-CONTOURS 



V-CONTOURS 



T^-CONTOURS 



Fig. 6. Shoaling on a shelf (oscillatory waves) 



164 



