1 + 



o , o 



2n 



which has the solution 



Cso) 



Thus, an explicit solution for the linearized friction factor in 

 terms of the breakwater geometry, the incident wave characteristics 

 and the hydraulic properties of the porous medium (a and 6), has been 

 obtained. 



The problem of determining f and hence the reflection and trans- 

 mission coefficients of a rectangular crib-style breakwater has there- 

 fore been reduced to the problem of determining the appropriate values 

 of the constants a and 3 in the Dupuit-Forchheimer relationship for 

 flow resistance in a porous medium. Engelund (1953) suggested the 

 following empirical formulas based on a review of several investigations 

 involving porous media characterized as sands. 



(51) 



and 



1-n ^ 

 3 d 



(52) 



in which v is the kinematic viscosity of the pore fluid and d is a 

 characteristic diameter of the porous material.. These relationships 

 are essentially of the type also suggested by Bear, et al. (1968). 

 Engelund (1953) proposed the values of the constants ex and S to be 







780 < a < 1,500 or more 



— o — 



1.8 < B < 3.6 or more . (53) 



— o — ^ ■' 



The constant a which is associated with a flow resistance linear 

 with velocity expresses a Darcy-type resistance, i.e., laminar, whereas 

 3 is associated with a turbulent resistance. Introducing equations 

 (51) and (52) in equation (48), this may be written: 



29 



