This energy dissipation consists of two separate components; one is 

 associated with the flow within the porous structure (the internal 

 energy dissipation) , and the other is associated with the energy dissi- 

 pation on the seaward slope (the external energy dissipation) . 



Section II of this report discusses, in an idealized manner, the 

 internal energy dissipation by considering the problem of the interaction 

 of waves and a homogeneous porous structure of rectangular cross section. 

 This problem was treated by Sollitt and Cross (1972) who presented a 

 review of previously published analytical studies of the problem. The 

 present approach, which was published by Madsen (1974), follows the 

 approach of Sollitt and Cross (1972) but arrives at an explicit analyt- 

 ical solution for the linearized flow resistance of the porous medium, 

 thus circumventing Sollitt 's and Cross' tedious iterative procedure 

 which involved the use of high speed computers. Furthermore, empirical 

 relationships relating the flow resistance of a porous medium to stone 

 size and porosity are suggested and the final result is an explicit 

 analytical solution for the reflection and transmission coefficients 

 of rectangular breakwaters. This solution is tested against the experi- 

 mental observations of Wilson (1971) and Keulegan (1973), and found to 

 yield quite accurate results. The explicit solution may also be used 

 to assess the severity of scale effects in model tests with porous 

 structures. 



Section III of this report discusses the problem of the energy 

 dissipation on the seaward slope of a porous breakwater by considering 

 the associated problem of energy dissipation on a rough impermeable 

 slope. Since the stone size below the cover layer of a trapezoidal, 

 raultilayered breakwater is generally quite small, the seaward slope 

 will essentially act as an impermeable rough slope. With the assumption 

 of nonbreaking waves the energy dissipation on the rough slope is 

 expressed by accounting for the bottom frictional effects. An analytical 

 solution for the reflection coefficient is obtained and the bottom fric- 

 tion, which is linearized, is related to a wave friction factor by 

 invoking Lorentz' principle of equivalent work. To evaluate this solu- 

 tion it is necessary to have an empirical relationship for this wave 

 friction factor. Such an empirical relationship is established experi- 

 mentally for rough slopes whose roughness is adequately modeled by 

 gravel, i.e., natural stones. The experiments reveal the need for an 

 accurate method for the determination of reflection coefficients from 

 experimental data. Such a method is developed and the semiempirical 

 procedure for estimating the reflection coefficient of rough impermeable 

 slopes is tested against a separate set of experiments. The procedure 

 yields accurate results and is believed to present a physically more 

 realistic approach to this problem than the semiempirical method 

 presented by Miche (1951). 



Section IV of the report synthesizes the results obtained in 

 Sections II and III into a rational procedure for the estimate of reflec- 

 •''"'on and transmission coefficients of trapezoidal, multilayered break- 



