160 BREAKER DIRECTION AND HEIGHT 



and the only change in their heights there, as they near the breaker 

 line, is such as may be directly due to their advance over the shoaling 

 bottom. But it is evident that the waves offshore might be at a con- 

 siderable angle with the coast around the flanks of a beach of this 

 shape ; hence they would be refracted there to a degree depending on 

 the precise shape of the coast, on the contour of the bottom, and on 

 the initial shapes and dimensions of the waves, as explained above 

 (p. 155). 



Calculation of the precise amounts by which refraction affects the 

 heights of waves at successive places around a curving coastline in- 

 volves tedious computations. But the approximate amount of reduc- 

 tion, from refraction, to be expected from place to place, for waves 

 of different degrees of steepness, may be taken directly from table 

 37, if one first marks on the chart the general trend of the wave crests 

 offshore, and then measures the angle at different places between the 

 latter and the depth line where surf is to be expected with waves of the 

 heights that are running at the time. In the case, for example, that 

 is represented above in figure 47, where the wave crests offshore are 

 parallel with the central sector of the bay, but make an angle of about 

 40° with its flanks, refraction would tend to reduce their heights by 

 about 10 to 12 percent at the points marked B and C by the time they 

 broke, if they were 20 to 100 times as long as high while still out in 

 deep water, and if they broke where the depth was equal to 1.3 times 

 their own heights at that moment, but by only 6 percent if they were 

 only 10 times as long as high to begin with. Reduction of the wave 

 heights by refraction would naturally be greater along the more 

 sheltered of the 2 flanks of the beach, if the waves were coming in at 

 a considerable angle with its central sector. This is illustrated by 

 the lower diagram (fig. 47), where the height of the breakers to be 

 expected would only be about half as great at the point B — other things 

 being equal — as at the point C. And the more abrupt the curvature 

 of a beach is, the more likely it is that the angle at which the waves 

 are coming in will be so great, off one or other of its flanks, that the 

 reduction of breaker height by refraction will be considerable there. 



It is necessary, however, to remember that this tendency for a wave 

 to decrease in height, as it is refracted around toward the coast, may 

 be more than offset by the opposite tendency, i.e., for it to increase in 

 height, as it advances shoreward over the shoaling bottom. These 

 two opposing tendencies must therefore be balanced one against the 

 other before one can judge whether landing on an open curving 

 beach will be aided much by refraction at any given time. Under 

 the circumstances that are illustrated, for example by the upper dia- 

 gram in figure 47, any reduction by refraction would be more than 

 counterbalanced in that way, unless the waves were steeper than about 



