Van Mater and Neat 



include change of wave form with wave slope symmetry retained, 

 wave asymmetry about the horizontal plane, wave peak- up, wave 

 breaking, wave height attenuation after breaking, stability of the 

 reforming waves, wave refraction along paths other than normal to 

 the bottom contours, bottom friction, and surface contamination. 

 Excluded are: wave slope asymmetry and change of wave form close 

 to breaking, wave set-up and set-down, the presence of caustics, 

 bottom percolation and internal friction, wave reflection, non-linear 

 decomposition, and solotonic shedding. The system will not be 

 carried all the way into the beach. 



Specifically, a linear theory for impulsively- gene rated waves 

 in water of uniform depth is invoked to describe the waves in deep 

 water at a large distance froin the source. From this point a 

 different linear theory based on conservation of energy per unit 

 frequency is employed to depict the system as it moves into a region 

 of shoaling topography. The integral expressions in this theory are 

 evaluated numerically using the conditions at each of a series of 

 closely- spaced stations as input for evaluating conditions at the next 

 station. As the system progresses into shallow water its frequency- 

 dispersive nature gradually disappears and non-linear features 

 dominate in the wave form and propagation velocities. A non-linear 

 cnoidal wave theory is matched numerically to the previous solutions 

 to carry the system in this region. The cnoidal theory is used to 

 describe the profiles of the individual waves in the system and the 

 asymmetry of the system about the horizontal plane. To treat wave 

 breaking existing experimental evidence has been reexamined and 

 an improved criterion for wave breaking is incorporated. From the 

 same experimental source empirical formulations are developed to 

 account for wave height attenuation after breaking and the attainment 

 of stability in the reforming wave. The Van Dorn formula for bottom 

 friction and surface contamination is used to account for these effects. 

 The system is computed not only along an cixis normal to the bottom 

 contours but also along a series of rays which emanate radially 

 from the source and change direction continuously due to refraction 

 as the waves move inshore over the shoaling water. 



All these features have been incorporated in a computer pro- 

 gram. Results of this program for a specified bottom profile and 

 for several source strengths are presented as figures. For the 

 researcher working on similar type problems perhaps the most useful 

 part of the paper will be the computational procedure which is dis- 

 cussed in some detail in an appendix. 



II. WAVE GENERATION 



Treatment of the subject of water waves produced by a local 

 disturbance has a long history beginning with Cauchy [ 1815] and 

 Poisson [ 1816] each of whom independently solved the classic two- 

 dimensional wave problem which bears their names. In recent 



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