ON THE PREDICTION OF IMPULSIVELY 



GENERATED WAVES PROPAGATING INTO 



SHALLOW WATER 



Paul R, Van Mater, Jr. 



United States Naval Academy 

 Annapolis J Maryland 

 and 

 Eddie Neal 

 Naval Ship Research and Development Center 

 Washington^ B.C. 



ABSTRACT 



This report treats the problem of the propagation of a 

 dispersive wave system generated impulsively by a 

 surface explosion in deep water into shoaling and shallow 

 water regions. A topography consisting of an arbitrary 

 bottom profile with parallel straight contour lines is 

 assumed. The linear theory of impulsive wave genera- 

 tion for water of uniform depth is used as a basis for 

 evaluating the spectral energy of the wave system at a 

 point in deep water distant from the explosion. Con- 

 sejrvation of energy is then invoked to extend the pre- 

 diction to propagation over a bottom of variable depth. 

 A cnoidal wave theory is introduced to describe the 

 changes in form of the individual phase waves and the 

 wave envelope as the system enters the shallow water 

 regime. The effect of wave refraction at locations 

 other than along an axis normal to the bottom contours 

 is treated. Empirical criteria are incorporated to pre- 

 dict the occurrence of wave breaking, the decay of wave 

 height after breaking, and the attainment of stability 

 in the reforming wave. Attenuation of wave height due 

 to dissipation of energy at the fluid boundaries is also 

 considered. All of the above elements have been in- 

 corporated in a computer program. Details of the 

 computational procedure are described in an appendix. 

 Typical predictions made using this program are dis- 

 played for small, moderate, and large source strengths. 

 The agreement of the predictions with experimental 

 observations is discussed qualitatively, but no experi- 

 mental data are included. 



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