II. TRANSMISSION AND REFLECTION CHARACTERISTICS 



OF RECTANGULAR CRIB-STYLE BREAKWATERS 



1. Preliminary Remarks. 



This section presents a theoretical treatment of the problem of 

 wave transmission through and reflection from a porous structure of 

 rectangular cross section. The basic assumptions are: 



(a) Relatively long normally incident waves which are considered to be 

 adequately described by linear long wave theory. 



(b) The porous structure is homogeneous and of rectangular cross 

 section. 



(c) The flow resistance within the porous structure is linear in the 

 velocity, i.e., of the Darcy-type. 



The essential features of the derivation and mathematical manipu- 

 lation of the governing equations are presented in Appendix A to enable 

 the treatment to be relatively brief and to the point. The theoretical 

 solution for the transmission and reflection coefficient is obtained 

 based on the above assumptions and results in a solution which depends 

 on the friction factor arising from the linearization of the resistance 

 law, which for prototype conditions may be expected to be quadratic 

 rather than linear in the velocity. 



A flow resistance of the Dupuit-Forchheimer type (Bear, et al., 

 1968) is assumed, and an empirical relationship relating flow resistance 

 to stone size, porosity, and fluid viscosity gives a fair representation 

 of experimentally observed hydraulic properties of porous media. 

 Adopting this empirical formulation of the flow resistance for a porous 

 medium in conjunction with Lorentz' principle of equivalent work leads 

 to a determination of the linearized flow resistance factor in terms of 

 the characteristics of the porous material and the incident wave 

 characteristics. In this manner an explicit solution for the reflection 

 and transmission coefficients for a crib-style breakwater is obtained. 



Knowledge of the incident wave characteristics, the breakwater 

 geometry, and the characteristics (stone size and porosity) of the 

 porous material is sufficient for the prediction of reflection and 

 transmission coefficients. The procedure was tested against experi- 

 mentally observed reflection and transmission coefficients (Keulegan, 

 1973; Wilson, 1971) and yielded accurate predictions of transmission 

 coefficients; the reflection coefficients are less accurately predicted. 

 The discrepancy between predicted and observed reflection coefficients 

 may be partly attributed to experimental errors in the determination of 

 reflection coefficients. 



