must be computed from Equation 2-2; in shallow water, tanh(2Trd/L) becomes 

 nearly equal to 2TTd/L and Equation 2-2 reduces to Equation 2-9. 



^2 _ 



gd or C = (gd)*^ . (2-9) 



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 



8 



(2-38) 



It has been noted that not all of 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 negligible. 



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

 shore, no energy flows laterally along a wave crest; that is 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 



^o = \KK^o' (2-73) 



where h^ 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 = nbEC, (2-74) 



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

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



\/b„\/C„\ 



(2-75) 



From Equation 2-39, 





(2-76) 



2-66 



