Impulsively Generated Waves Propagating into Shallow Water 



Van Dorn, W. G. and Montgomery, W. S. , Scripps Inst. Ocean. 

 Ref. 63-20, 1963. 



Van Mater, P. R. , Nav. Ship Res. and Dev. Ctr. Rpt. 3354, 1970. 



Whalin, R. W. , "Water Waves Produced by Underwater Explosions: 

 Propagation Theory for Regions Near the Explosion," 

 Jour. Geophysical Res., v. 70, n. 22, 1965a. 



Whalin, R. W. , Nat. Engr. Science Co. Rpt. S 256-2, 1965b. 



Wiegel, R. L. , Oceanographical Engineering , Prentice Hall, 1964. 



APPENDIX 1 

 COMPUTATIONAL PROCEDURE 



This appendix discusses the details of implementing the theory 

 outlined in the previous sections in a computer program which will 

 predict the wave system in shallow water. 



Initially, a monotonically decreasing bottom profile is 

 assumed with parallel straight bottom contours as shown in Fig. 4. 

 Actually, the specific profile used in this program was chosen to 

 conform to that of a test basin at the U.S. Army Engineer Waterways 

 Experlnnent Station, Vicksburg, Miss, in order to permit comparison 

 of the analytical predictions with experiments performed there. A 

 polar coordinate system is established with the origin at the point of 

 the explosion and the axis taken normal to the bottom contours. The 

 axis is divided into a number of closely spaced stations, indexed i, 

 with i = at the origin. The frequency range of interest is also 

 divided into a number of closely spaced frequencies, indexed j. 

 A number of rays, or orthogonals , indexed k, are established 

 emanating from the origin. The local angle of the orthogonal with 

 the normal to the bottom contours varies with the frequency, u), and 

 the water depth at a given location is identified as Ojjk^ Because of 

 the frequency dependence absolute congruence of the trajectories of 

 the orthogonals is not possible. To give the best overall conformity 

 with respect to both location and path length the initial angle of the 

 orthogonal at the origin, Oojk » ^s adjusted with frequency. Thus the 

 index k identifies a family of orthogonals which have approximate 

 but not precise spatial agreement, except, of course, on the axis. 

 Throughout indexical notation is for array identification only and 

 tensor convention is not implied. 



A starting station, 1=1, is selected in deep water sufficiently 

 distant from the explosion for Eq. (4) to be valid. That theory strictly 



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