diverge, resulting in low heights at the shore. (b^i/b less than 1.0.) 

 Similarly, heights will be greater at a headland than in a bay. Since 

 the wave energy contained between two orthogonals is constant, a larger 

 part of the total energy expended at the shore is focused on projections 

 from the shoreline; consequently, refraction straightens an irregular 

 coast. Bottom topography can be inferred from refraction patterns on 

 aerial photography. The pattern in Figure 2-17 indicates the presence 

 of a submarine ridge. 



Refraction diagrams can provide a measure of changes in waves 

 approaching a shore. However, the accuracy of refraction diagrams is 

 limited by the validity of the theory of construction and the accuracy 

 of depth data. The orthogonal direction change (Equation 2-78) is 

 derived for straight parallel contours. It is difficult to carry an 

 orthogonal accurately into shore over complex bottom features (Munk and 

 Arthur, 1951). Moreover, the equation is derived for small waves moving 

 over mild slopes. 



Dean (1973) considers the combined effects of refraction and shoal- 

 ing including nonlinearities applied to a slope with depth contours 

 parallel to the beach but not necessarily of constant slope. He finds 

 that non-linear effects can significantly increase (in coirparison with 

 linear theory) both amplification and angular turning of waves of low 

 steepness in deep water. 



Strict accuracy for height changes cannot be expected for slopes 



steeper than 1:10, although model tests have shown that direction 



changes nearly as predicted even over a vertical discontinuity (Wiegel 

 and Arnold, 1957). Accuracy where orthogonals bend sharply or exhibit 

 extreme divergence or convergence is questionable because of energy 

 transfer along the crest. The phenomenon has been studied by Beitinjani 

 and Brater (1965), Battjes (1968) and Whalin (1971). Where two ortho- 

 gonals meet, a caustic develops. A caustic is an envelope of ortho- 

 gonal crossings, caused by convergence of wave energy at the caustic 

 point. An analysis of wave behavior near a caustic is not available; 

 however, qualitative analytical results show that wave amplitude decays 

 exponentially away from a caustic in the shadow zone, and there is a 

 phase shift of it/2 across the caustic (Whalin 1971). Wave behavior 

 near a caustic has also been studied by Pierson (1950), Chao (1970) and 

 others. Little quantitative information is available for the area 

 beyond a caustic. 



2.328 Refraction of Ocean Waves . Unlike Monochromatic waves, actual 

 ocean waves are more complicated. Their crest lengths are short; their 

 form does not remain permanent; and their speed, period, and direction 

 of propagation vary from wave to wave. 



2-78 



