37 



Using the trochoidal theory formula for E, the height is obtained 

 from equation 43, since: 



£=H|^(^1_mA:)=^ (37) 



Neglecting the quantity in parentheses, the approximate height is 



VwCg 

 Usmg this value of h' in the parentheses, 



^'=v4 ^''^ 



8Po 



h=^ „ SPM . (46) 



V ^^"^ {U-Mh') 



The period T is assumed to be constant, Po is known from the period 

 and height in deep water and L, M, and (?<? are fixed by the period 

 and depth, figures 2, 12, and 13. 



C 



Since — ^ approaches unity as the depth decreases, the value of h 



obtained from equation 46 will differ from that obtained from equa- 

 tion 38, which is based on the assumption that one-half of the energy 

 travels with the wave form. Comparison of the heights predicted by 

 equations 38 and 46 with experimental results should be decisive as to 

 which concept of the energy transmission is correct. 



If it is found that the wave velocity is appreciably affected by wave 

 height, the quantities already obtained can be corrected, starting 

 from the relationship L=ChT. The corrected value of L is then inserted 

 in equation 46 in solving for A. It appears unlikely that the effect of 

 finite height on velocity need be considered in engineering compu- 

 tations. 



The computations cannot be carried as far as the plunge point. 

 Independent experiments on the depth in which waves break must 

 be relied upon for this limit. Insofar as the theory is concerned, the 

 only limitation supplied is that the angle at the crest should not be less 

 than 120°. 



Dissipation of energy by internal and bottom friction before the 

 wave reaches the outer line of breakers is assumed to be negligible. 

 No assumption regarding reflection of the waves has been made but 

 an experimental check on the theory would require that the energy 

 be completely absorbed in order to permit accurate measurement of 

 height and length. 



Section 7. WAVE REFRACTION 



The refraction of waves running obliquely on a shore line is a well- 

 known phenomenon. At the line of breakers, the wave crests seldom 

 make an angle of more than 15° with the shore line even when the 

 crests in deep water are almost perpendicular to the shore. This 



