Per the left side, <L/L ~ 0.2865. Making use of the tables (Ref. 11 ) it is 

 found that d±/h s 0.3000$ henee, L = 0.071/0.3000 s 0.237 ft. as compared with 

 the measured wave length, L s 0.24 ft. For the right side of the channel, d n 

 0.027, d/L s 0.1090; hence d/L = 0.1488 and L = 0.027/0.1488 r 0.181 ft. which 

 again was nearly the same as the measured -value of 0.184 ft. 



Wave Refraction 



TWhen waves approach a beach at an angle their crests are bent, because the in- 

 shore portion of the wave front travels in shallower water and hence, at a 

 lower velocity than does the portion in deeper water. The bottom topography, 

 the wave period and direction of travel in deep water determine the character- 

 istics of refraction in shoaling water. The result of refraction is a ohange 

 in wave height, length and direction of wave travel. The lengths of waves 

 travelling over a shoaling beaoh is decreased due to the decreased velooity 

 for L a C T, as T remains constant. The decreased wave length means also a 

 concentration of wave energy and, hence, an inorease of wave heights, for 



Pi m f Hi \ 



where P^ and P2 is the power per unit length of orest passing points 1 and 2 

 and H]_ and H, are the corresponding wave heights. 



Thus, waves travelling over a submarine ridge usually will be decreased in 

 length and increased in height and passing over a submarine valley will be 

 increased in length and decreased in height. 



To illustrate the refraction on a shoaling beaoh Run 6 (Figure 3a) was com- 

 pleted. A uniformly sloping beach with a slope of 1:13 was introduced with an 

 angle of 57° between the front of approaching waves and the parallel contour- 

 lines of the beach. The refraotion pattern can be seen clearly in the photo- 

 graph of Run 6. However, the best conception of this phenomena can be obtained 

 by observing the moving piotures taken with a speed of 48 frames per second 

 and then projecting them at about 1/3 of this speed. The increased heights of 

 the waves on the shore are indicated by the sharper crest-lines in the photo- 

 graphs. 



Runs 3, 4, and 5 (Figure 3a) illustrate the ohanges in wave lengths and veloeities 

 as the waves pass over shoals of various configurations. In Run 3 the waves 

 are passing over an abrupt triangular shoal; in Run 5 over an abrupt reotangular 

 shoal; while Run 4 demonstrates the wave characteristics when an abrupt "invert- 

 ed" triangular shoal is introduced. It might be stated that Runs 3 and 5 repre- 

 sent the wave phenomenon over a submarine ridge, while Run 4 is similar to the 

 wave characteristics over a submarine valley. Naturally the ohange of the depth 

 in the ocean usually is not so abrupt. This will ohange the oharaoteristios 

 only as far as the angle of intersection of wave orest-lines is ooncerned. 

 A gradual ohange of depth will introduce a gradual ohange in the direotlon of 

 wave travel, as oan be seen in Run 6, whioh demonstrates the refraction of 

 waves on a sloping beaoh. 



