Impulsively Generated Waves Propagating into Shallow Water 



irreversibly unstable and breaking follows. In the final 

 stage before breaking there is an abrupt increase in wave 

 height known as "wave peak- up. " Breaking may fall into 

 one of three broad categories: plunging, spilling, or 

 surging. 



(d) After breaking the wave continues as a spilling wave until 

 it either runs up on the beach or reforms as a stable 

 wave. Energy dissipation accompanying breaking reduces 

 the wave height. 



(e) In the case of dispersive systems entering shallow water 

 a low- frequency oscillation is superposed on the wave 

 train. This "wave set-up and set-down" is caused by the 

 transport of mass with the system, particularly when 

 breaking or near breaking occurs , and the resulting 

 counterflow, 



(f) When an element of a wave crest passes over a bottom 

 contour line obliquely it is refracted so as to be more 

 nearly aligned with the bottom contour line. If the bottom 

 contours are not parallel straight lines a focusing of 

 wave energy can occur at "caustic points" and consider- 

 able wave height enhancement can result, 



(g) The height of waves in shallow water is attenuated by 

 energy losses due to bottom friction, bottom percolation, 

 internal friction, and surface contamination. 



(h) Incoming waves which encounter steep offshore bars or 

 beaches may be reflected seaward. Under the right con- 

 ditions standing wave systems of surprising severity may 

 be produced. 



(i) Non-linear instabilities in a shallow-water wave may 

 cause it to decompose, or split into two or more com- 

 ponent waves. The hazardous "double rollers" are often- 

 times an example of this. A different type of decomposi- 

 tion may occur when a wave passes over an offshore bar 

 and nearly breaks but then recovers. One or more 

 smaller waves known as "solitons" may be shed from the 

 back of the larger wave. Little is known about these waves 

 at present. 



All of these features can affect ship and small craft operations 

 in shallow water and have been included to emphasize the complexity 

 of the overall problem. Not all will be attempted in the prediction 

 scheme presented in this paper. For our purposes we will consider 

 a wave system resulting from an explosion in deep water of nearly 

 uniform depth, which propagates into shallow water over a terrain 

 represented by parallel straight line bottom contours. We will 



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