the dissipation of energy associated with the top layer of stones in the 

 cover layer. The reamining wave energy may be expressed as the energy 

 associated with a progressive wave of amplitude, 



aj = Rjj a. , (146) 



in which a. is the amplitude of the actual incident wave, and Ry-, is the 

 reflection coefficient determined by the procedure developed in 

 Section III. 



With the energy dissipated on the seaward slope accounted for, the 

 remaining energy is partitioned betweeen reflected, transmitted, and 

 internally dissipated energy. This partition of energy is the problem 

 dealt with in Section II of this report,. and it is evaluated by regarding 

 the remaining energy as an equivalent wave of amplitude, a^, normally 

 incident on an equivalent homogeneous rectangular breakwater. The role 

 of this homogeneous rectangular breakwater is to reproduce the internal 

 energy dissipation associated with the trapezoidal, multilayered 

 breakwater, i.e., the two breakwaters should be hydraulically equivalent. 

 A rational method for obtaining a homogeneous rectangular breakwater 

 which is hydraulically equivalent to a trapezoidal, multilayered 

 breakwater is developed in Section IV. 2, based on steady flow consider- 

 ations. By using the procedure developed in Section II, the partition 

 of the remaining wave energy among reflected, transmitted, and 

 internally dissipated energy is therefore approximately evaluated by 

 determining the reflection coefficient, Rj , and the transmission 

 coefficient, Tj, of the hydraulically equivalent homogeneous rectangular 

 breakwater subject to an equivalent incident wave of amplitude, a,. 



Having now accounted for the external as well as the internal 

 energy dissipation the amplitude of the reflected wave is found to be 



l\l = ^I^I = ^I^^II^ ' ^'''^ 



and the transmitted wave amplitude is 



1^1 = -^I^I = ^I^II^i ■ ^'''^ 



The approximate values of the reflection and transmission 

 coefficients, R and T, of a trapezoidal, multilayered breakwater are 

 therefore 



RjRjj (149) 



81 



