Computation of the Motion of Long ^ater Waves 



The contour lines in Fig. 6 were computed by a plotting pro- 

 gram developed by Schreiber [ 1968] . The facility used was an IBM 

 2250 graphic display unit in which the computed contour lines are 

 projected on a TV screen. The contour plots were recorded by 

 photographing the surface of the screen. Several motion pictures 

 have also been made with this apparatus. 



Two 2250 units are used when films are made. First, as 

 noted above the computed field values are stored on tape during the 

 APPSIM2 computer run. Later, a special program calls up the 

 tapes and transforms the field data to contour lines. These are 

 transmitted to the 2250 units. One is used as a control console to 

 monitor picture quality and to set the movie camera speed. The 

 second unit has a 16 mm movie camera mounted on it and focused on 

 the screen. The camera operation is synchronized with the suc- 

 cession of contour plots flashed on the TV screen. Titles are also 

 constructed on the screen and filmed. Judicious editing transforms 

 the 16 mm film into a useful and interesting nnovle. As the sequence 

 of Fig, 6 shows, the evolution of the flow fields is particularly 

 instructive. Because all the pertinent parameters are usually shown 

 simultaneously on the screen with the contour plots, quantitative 

 interpretations of the contour information can be made directly 

 from the graphic display. For exannple, at t = 68.5 the maximum 

 wave height along the line y = Is about 0,06, while along y - ^z» 

 the height Is 0,05 (I, e. , the wave is unaffected by the shelf at this 

 time). In Fig. 6, the r|-plot Increment for t = 68.5 Is 0,01, the 

 maximum value is "n = 0,064 and the minimum. Is t) = - 0,026, For 

 oscillatory waves It Is necessary to have some detailed printout In 

 addition to the graphic display for quantitative analyses because the 

 contours are not marked with their contour level values. 



Finally, we simulated long wave amplification by a circular 

 submarine seamount and compared our results with the experimental 

 values of Williams and Kartha [ 1966] , The following pertinent param- 

 eters exactly match one of their experimental runs for a half-seamount 

 (Fig, lb) with non-dlmienslonal parameter X= 2Trb/Lo = 3,0: Xq= 56.7 

 Is the distance from the wave generator to the peak of the Island; 

 b = 7,73 Is the radius of the base of the seamount, T = 16,6 is the 

 wave period, "Hq = 0.0082, d = 1,0 beyond the seamount base, 

 € = 0.116 Is the submergence of the seamount at Its peak and 

 1-2 = 23,2. The tank length Lj = 116 was selected to prevent re- 

 flections from reaching the seamount. The amplification ratio 

 Hj/Hq = Af was calculated where Hq = Zy]^ and Hj = the trough-to- 

 crest distance on waves at the Island peak where d = € , 



The experimental Af = 2,42, while A^ = 2,46 according to 

 the refraction theory of Mogel , et al, [1970] and Af = 2.70 accord- 

 ing to APPSIM2 for a seamount whose shape was given by 



d(x,y) = (1.0 - €)(^)'' 



+ € 



165 



