with a .velocity 



lu I = (1-R) a. /|^ . (39) 



o 



Behind the structure the maximum surface elevation is given by 

 kJ=Ta. (40) 



with the horizontal velocity being 



|uj = T a. /^ (41) 







The above formulas disregard any phase difference between the re- 

 flected, incident, and transmitted waves and are therefore limited to 

 extremely narrow structures. 



Disregarding storage within the structure the velocities, |u | and 

 |u I, must be equal which leads to 



1 -R -T = . (42) 



To obtain an additional equation it is realized that the resistance 

 to the flow through the structure is balancing the pressure force on the 

 structure. This leads, with the linearized flow resistance introduced 

 previously, to 



f n ^'"J = ga + R -T) a. , (43) 



which for long waves, u = k i^gh and u. given by equation (41) lead to 



k Zf 



-^ 2T = 2XT = 1 + R -T , (44) 



in which A, as given by equation (34), has been introduced. Solving 

 equations (42) and (44) for T and R gives 



T = A_ 



1+A (45) 



and 



R = UX C46) 



27 



