Table 4-9. Assumptions for Pj Formulas in Table 4-8. 



1. Formula 1 — Equation 4-35 



a. Energy density at breaking is given by linear theory, 



E = (pg4)/8 « SHg 



b. Group velocity equals wave speed at breaking, and breaking speed is given by 

 solitary wave theory according to the approximation. (Galvin, 1967, Equation 11.) 



C^ = C«(2gHj,)^/^= 8.02 (Hfe)^/^ 

 c. a can be replaced by ay 



2. Formula 2 — Equation 4-36 



a. Same as lb above 



b. H, is related to H by refraction and shoaling coefficients, where the coefficients 

 are evaluated at the breaker position 



c. Refraction coefficient K^^ given by small-amplitude theory; shoaUng coefficient 

 K assumed constant, so that 



d. (Hj,)^/^ = 1.14 (cosaj'/^ h/^ 

 if (cosaj,)'/^ = 1.0 



and (Kj'/^ = 1.14 



3. Formula 3 — Equation 4-37 



a. Refraction coefficient at breaking is given by small-amplitude theory. 



4. Formula 4 — Equation 4-38 



a. Same as la above 



b. Same as lb above 



c. Same as 3a above 



d. Cos ttjj = 1.0 



NOTE: Constants evaluated for foot-pound-second units. Small-amplitude theory is assumed valid in 

 deep water. Nearshore contours are assumed to be straight and parallel to the shoreline. 



4-98 



