III. WAVE REFRACTION 



1. Introduction. 



Equation (2-2) shows that wave celerity depends on the water depth in 

 which the wave propagates. If the wave celerity decreases with depth, wave- 

 length must also decrease proportionally. Variation in wave velocity occurs 

 along the crest of a wave moving at an angle to underwater contours because 

 the part of the wave in deeper water is moving faster than the part in shal- 

 lower water. This variation causes the wave crest to bend toward alinement 

 with the contours (see Fig. 2-17). This bending effect, called refraction, 

 depends on the relation of water depth to wavelength. It is analogous to 

 refraction for other types of waves; i.e., light and sound. 



In practice, refraction is important for several reasons: 



(1) Refraction, coupled with shoaling, determines the wave height 

 in any particular water depth for a given set of incident deepwater 

 wave conditions; i.e., wave height, period, and direction of prop- 

 agation in deep water. Refraction therefore has significant influence 

 on the wave height and distribution of wave energy along a coast, 



(2) The change in wave direction of different parts of the wave 

 results in convergence or divergence of wave energy and materially 

 affects the forces exerted by waves on structures. 



(3) Refraction contributes to the alteration of bottom topography 

 by its effect on the erosion and deposition of beach sediments. Munk 

 and Traylor (1947) confirmed earlier work indicating the possible 

 interrelationships between refraction, wave energy distribution along 

 a shore, and the erosion and deposition of beach materials. 



(4) A general description of the nearshore bathymetry of an area 

 can sometimes be obtained by analyzing aerial photography of wave 

 refraction patterns. While the techniques for performing such analy- 

 ses are not well developed , an experienced observer can obtain a gen- 

 eral picture of simple bottom topography. 



In addition to refraction caused by variations In bathymetry, waves may be 

 refracted by currents or any other phenomenon that causes one part of a wave 

 to travel slower or faster than another part. At a coastal inlet, refraction 

 may be caused by a gradient in the current. Refraction by a current occurs 

 when waves intersect the current at an angle. The extent to which the current 

 will refract incident waves depends on the initial angle between the wave 

 crests and the direction of current flow, the characteristics of the incident 

 waves, and the strength of the current. In at least two situations, wave 

 refraction by currents may be of practical importance. At tidal entrances, 

 ebb currents run counter to incident waves and consequently increase wave 

 height and steepness. Also, major ocean currents such as the Gulf Stream may 

 have some effect on the height, length, and direction of the approach of waves 

 reaching the coasts. A quantitative evaluation of the effects of refraction 

 by currents is difficult. Additional research is needed in this area. No 

 detailed discussion of this problem is presented here, but an introduction is 

 presented by Johnson (1947). 



2-60 



