************** EXAMPLE PROBLEM ************** 



GIVEN : A deepwater oscillatory wave with a wavelength of L^ = 512 feet, 

 a height of H^ = 5 feet and a celerity of C^^ = 51.2 ft/sec, moving 

 shoreward with its crest parallel to the depth contours. Any effects 

 due to reflection from the beach are negligible. 



FIND : 



(a) Derive a relationship between the wave height in any depth of water 

 and the wave height in deep water, assuming that wave energy per 

 unit crest width is conserved as a wave moves from deep water into 

 shoaling water. 



(b) Calculate the wave height for the given wave when the depth is 10 

 feet. 



(c) Determine the rate at which energy per unit crest width is trans- 

 ported toward the shoreline and the total energy per unit width 

 delivered to the shore in 1 hour by the given waves . 



SOLUTION : 



(a) Since the wave crests are parallel to the bottom contours, refraction 

 does not occur, therefore H^ = H^. (See Section 2.3. WAVE 

 REFRACTION.) 



From Equation 2-43, 



8 



where H^ represents the wave height in deep water if the wave 

 were not refracted. 



Substituting into the above equation gives. 



2-29 



