158 



BREAKER DIRECTION AND HEIGHT 



And the inshore ends tend to lost height in consequence, because the 

 energy that the waves carry with them is spread through a longer 

 distance by this alteration. Theoretically, this decrease in height 

 is inversely proportional to the amount of side wise expansion. 46 And 

 since the amount by which a wave crest is expanded sidewise in this 

 way depends on how much it has been refracted, it follows that the 

 greater the angle is between the wave in deep water, and the coast, the 

 more the wave tends to lose height as it is refracted around. Table 37 



iV>A**-WitX 



0.30 



Figure 46. — Diagram to illustrate the refraction of waves along a straight shore 

 line, when the wave crests in deep water form an angle of 70° with the coast. 

 The depths of the bottom contours are given in terms of the offshore wave 

 length. The wave crest at the left has been plotted by the simplified procedure 

 described on page 157. The arrows indicate the lines of advance of the waves at 

 successive points along their crests. 



shows the theoretical loss in height by refraction for waves of different 

 degrees of steepness, coming in at different angles. 



Multiplication of the heights offshore by the ratio given in the ap- 

 propriate column of table 33 (p. 121) will give the approximate height, 

 at breaking, for waves of varying degrees of initial steepness, coming 

 in parallel with the shore. And a further correction of the heights 

 calculated in this way, using the percentages given in table 37 will 



** According to the equation: H = H ^jr i> '- where Ho is the height of the wave over 

 deep water ; H, its height when it strikes the beach ; dlo, the sidewise extent of a given 

 segment of its crest over deep water ; and dl, the sidewise extent of this same segment of 

 its crest at any given point during its advance shoreward. But the few pertinent observa- 

 tions indicate that waves which have been refracted through large angles are somewhat 

 higher than indicated by this equation, suggesting a flow of energy sidewise along their 

 crests. There is reason to believe that the effect of refraction is slightly different for 

 waves of different steepness, but the matter has not been studied in detail. 



