128 Shallow Water Wave Transformation through External Factors 

 deflection is a, the wave height will decrease by 



hz\h x == 1-006) a 



provided the deflected waves can expand freely. However, if the waves, after 

 having been deflected, move by the breakwater without hitting it, we have 



h 2 :! h = 1-1-04 ya 



(see Forchheimer, 1924, p. 378). 



Orthogonois 



A 



Contours 



Slight (Divergence along entire coast-line 



~— — - — ■ ~ 



'MV///-V// 



Shore line 



Fig. 59. Refraction of waves along beach with straight parallel depth contours. The wave 



crest along the orthogonal B is always in deeper water than along A and therefore moves 



with greater velocity. As a result, the waves tend to turn parallel to the shore. 



Blaton (1937) was the first who attempted to give a theoretical ex- 

 planation by transposing similar problems from geometrical optics to grav- 

 itational waves, in applying the principle of Fermat. Munk and Traylor 

 (1947) have investigated this problem thoroughly and were able to devise 

 a theory for forecasting purposes. 



The process of refraction for a beach with depth contours running parallel 

 to the shore is governed by Snellius's Law 



sin a 

 sina 



c 



Co 



(V.23) 



in which a is the angle between the wave crest and the contours at any depth 

 and c the wave velocity at the same depth under consideration; the parameters 

 with subscript refer only to deep water, where the direction and the velocity 

 of the waves are constant. 



If the topography of the bottom is more complicated for which the depth 

 contours are neither straight nor parallel, the changes in the direction of 



