656 



[chap. 18 



fact that we treated only the case of normal incidence is of no great con- 

 sequence ; the derivation is easily generalized to allow for oblique incidence. In 

 the presentation of Fig. 7, the space between the ordinate and the diagonal is 

 devoted to the shelf waves (or "continuum" or "leaky" modes). At one extreme 

 is the normal incidence, corresponding to infinite wavelength (and hence zero 

 wave number n) along shore. The resonances discussed in section 5-A of this 

 Chapter correspond to the intersection of the lines marked "max" with the 

 frequency axis. For incidences other than normal, the resonance frequencies 

 increase somewhat, but not much. At the other extreme is the case of glancing 

 incidence ; that is, in deep water, h~H, the waves travel in a direction parallel 

 to shore, and the crests are normal to shore. Between normal and glancing 

 incidence there is a critical case indicated by the dashed line : for incidence 



Fig. 7. Schematics of the /, /i-diagram. Here / is the frequency, and n the wave-number 

 component along shore. 



more nearly glancing, the wave amplitude at the shoreline is less than in deep 

 water, whereas for incidents more nearly normal there is shoreward amplifica- 

 tion. 



This part of the/, ?i-diagram has been labelled "continuum", for every point 

 on this diagram is a possible solution to the wave equation, and corresponds to 

 some combination of frequency and angle of incidence. The other part of the 

 diagram corresponds to the discrete spectrum (or normal modes, or eigenvalues, 

 or edge waves, or "trapped" modes). The only possible combinations of fre- 

 quency and wave number are along a series of distinct curves, corresponding to 

 the fundamental and various harmonics. The discrete spectrum is characterized 

 by the fact that, in deep water, the wave amplitude diminishes with increasing 

 distance from shore, and essentially vanishes at a distance of a wavelength, 



