velocity must be computed from equation (2-2); in shallow water, tanh(2ird/L) 

 becomes nearly equal to 2Trd/L and equation (2-2) reduces to equation (2-9). 



C2 = gd or C = (gd) 



1/2 



Both equations (2-2) and (2-9) show the dependence of wave velocity on depth. 

 To a first approximation, the total energy in a wave per unit crest width may 

 be written as 



E = 



8 



It has been noted that not all the wave energy E is transmitted forward 

 with the wave; only one-half is transmitted forward in deep water. The amount 

 of energy transmitted forward for a given wave remains nearly constant as the 

 wave moves from deep water to the breaker line if energy dissipation due to 

 bottom friction (K^ = 1.0), percolation, and reflected wave energy is negli- 

 gible. 



In refraction analyses , it is assumed that for a wave advancing toward 

 shore, no energy flows laterally along a wave crest; i.e., the transmitted 

 energy remains constant between orthogonals. In deep water the wave energy 

 transmitted forward across a plane between two adjacent orthogonals (the 

 average energy flux) is 



P = 4- b E C (2-73) 



o 2 o o o 



where b is the distance between the selected orthogonals in deep water. 

 The subscript o always refers to deepwater conditions. This power may be 

 equated to the energy transmitted forward between the same two orthogonals in 

 shallow water 



P = nb EC (2-74) 



where b is the spacing between the orthogonals in the shallower water. 



Therefore, (1/2) b E C = nb EC, or 



o o o ' 



E l/l\f^W^o 



E 

 o 



From equation (2-39), 



2VnAb/VC' (2-^5) 



(2-76) 



and combining equations (2-75) and (2-76), 



i'JmiMM^ 



(2-77) 



2-63 



