680 



BARBER AND TUCKER 



[CHAr. 19 



using arguments like those of optical refraction. It has proved possible to obtain 

 an analytic expression for the rays refracted around a circular island or a 

 shoal that has circular symmetry (Arthur, 1946). 



002 0004 



02 04 0.8 



0.01 " ' " 0.1 



RATIO WATER DEPTH TO DEEP WATER WAVELENGTH, hJLo 



Fig. 8. If waves travel from deep water to shallow water their frequency is unaltered but 

 other characters change. The curves show how, starting from deep water on the right 

 of the graph, the wave velocity, wavelength and group velocity all grow less as the 

 wave enters shallower water towards the left of the graph. The accompanying increases 

 in wave height and wave steepness are calculated assuming the waves to be incident 

 normally on a straight coast (no refraction) and assuming that the waves remain low 

 enough to have a sinusoidal profile. The orbits of particles on the surface become more 

 and more elliptical, as indicated by the decreasing ratio of wave height to "range" or 

 horizontal excursion. The fluctuating water pressure on the sea-bed is negligible in 

 deep water but in shallow water tends to equal the water height directly above. 



Some curious refraction effects have been observed on the very exposed 

 Californian coast near La Jolla (Munk and Traylor, 1947). Two branches of a 

 submarine canyon here approach the coast quite closely and, because swell can 

 travel along them more quickly, the water being deeper, the wave energy is 

 refracted towards the shallower waters ; consequently the height of surf can 

 vary greatly along this coast. Fig. 7 illustrates these results. 



