Impulsively Generated Waves Propagating into Shallow Water 



The path length and offset from the axis are given by 

 i 



'i'jk - 2j ■^^7"^^— ~ <^^^ 



'_j »_OS 9: I i 1, 



yiiK=I ^«'-'^e.. ,_._,. (57) 



The system is tested for wave breaking by applying Eq. (19) to the 

 envelope height, Hjjk , increased by a factor of 1,40 to account for 

 non-linear peak up. If the test succeeds and breaking occurs then 

 the increased value of envelope height is retained as Hjj for use In 

 computing decay after breaking, Eq. (20), and wave stability, Eq. 

 (21). Indexing the breaking point as i = b and any location in the 

 surf zone beyond the breaking point as i = a, these equations become: 



H..= H,,(|.j-"-=^(^) . (58, 



^ Stable bjk S 



Once stability is found the envelope height, or rather the symmetrical 

 envelope elevation B = H/2 is carried forward in the usual way. 



Since the test for breaking is applied to the envelope, strictly, 

 wave breaking can be considered to occur only if a phase wave crest 

 occurs within the breaking band of frequencies. As a practical matter 

 the prediction of the exact arrival of the phase wave is the most 

 difficult and least reliable part of the whole procedure, so that the 

 surf zone should be considered to extend over any region where 

 breaking is predicted for any frequency within the envelope. 



The boundary dissipation equation, Eq. (22), is applied to the 

 envelope height between successive stations outside the breaking zone. 



In the present computation the array consists of 100 stations, 

 120 frequencies, and 3 fannilies of wave rays (Oq = 0°, 20°, 40°). 

 The computer program is listed in Van Mater [ 1970] . The program 

 requires 23 minutes of running time on the IBM 7094 and provides 

 about 14,000 lines of output. 



271 



