a(Eo ) 



sf- s pgQ 



'(*1 



Y 2/ 



\3' 



4Y Y 

 12 



(39) 



where 



p = water density 

 Q = flow across the jump 

 Y« = water depth on the high end of the jump 

 Y2 = water depth on the low end of the jump 

 For water of uniform depth, they assumed that Y2 = h + H and Y^ = h + BH 

 where 6 is a coefficient related to the percentage of the wave height 

 covered by foam. Battjes and Janssen (1978) also used a hydraulic jump repre- 

 sentation of wave breaking. They used the following expression: 



3(Ec ) „2 



-iT 8 - = **pg Q St (4o) 



where a* is a coefficient of order one. Mizuguchi (1980) modeled surf zone 

 energy loss as, 



3(Ec ) 



= 2pg v 



M) 



3x ° e 



where v is a coefficient of turbulent eddy viscosity. Results derived from 

 this model compared quite well with experimental data, but any physical rea- 

 soning behind the use of the eddy viscosity formulation is, as Mizuguchi 

 ( 1980) states, obscure. Horikawa and Kuo ( 1966) developed an analytical 

 scheme using second order solitary wave theory and theoretical expressions for 

 dissipation due to bottom friction and turbulence. Their governing equation 

 contained two coefficients, one for each dissipative mechanism. 



36. The transformation algorithm selected for use in RCPWAVE (Dally, 

 Dean, and Dalrymple 1984) uses the same energy flux basis as the models men- 

 tioned above. However, instead of using a hydraulic jump to represent energy 

 loss in a single breaking wave, the form of the hydraulic jump energy loss is 

 used to approximate losses across the entire surf zone. Through analogy with 

 energy flux in a channel, the following equation is postulated: 



3(Ec ) 



g_ 



3x 



>h-h)J 



21 



