Shallow Water Wave Transformation through External Factors 127 



A special topography of the beach can produce a repeated surf. The water- 

 mass which broke during the first surf process moves on over the beach as 

 a rather low wave, which can break again when the depth decreases more. 

 This action can even repeat itself. Figure 58 gives, according to Kriimmel, 



Fig. 58. Multiple surf ( W» to W h ). Rip current at bottom (Kriimmel). 



a picture of such a repeated surf. Associated with such a surf is a "rip cur- 

 rent", which is a current particularly strong at the bottom, and which carries 

 from the beach towards the sea any objects that are not fixed to the bottom. 

 (b) Refraction of Ocean Waves 



The preceding explanations refer to waves which travel towards the shore 

 and whose crests are parallel to the depth contours of the beach, and their 

 direction of propagation remains constant. This is no longer the case when 

 they approach the coast at an angle. The wave crests then tend to turn 

 parallel to the shore. The reason is that the wave velocity decreases with 

 decreasing depth, so that the part of the wave crest nearest to the shore 

 moves slower than the crest in deeper water which races ahead. Figure 59 

 makes this clear. This endeavour of the crest line to become, parallel with 

 the coast is similar to the one causing the bending of light rays in optical 

 systems. It is called wave refraction. 



Gaillard (1904, p. 66) and Stevenson (1864, p. 165) observed the 

 changes which waves undergo on account of different contours of the coast. 

 Gaillard found that a wavy coastline may cause a decrease in swell, in view 

 of the tendency of the waves to establish the wave front parallel to the coast 

 and consequently to stretch their crests. The swell is becoming less pronounced 

 when it moves into a harbour through a narrow opening. If b is the width 

 of the opening, an arc-shaped diffraction wave is formed, which at the dis- 

 tance m from the entrance has a radius m. If this arc has the length B, the 

 ratio between the later and the earlier wave height, according to Stevenson, is 



v-, 



•0-0269 1 + 



| m 



T Bj 



(everything in m). If waves are deflected by a breakwater and the angle of 



