Battjes (1978) argued that a constant y ratio across the surf zone in- 

 troduces an unrealistically high sensitivity in all the longshore current 

 models to variations in bottom profile. A constant y is also not applicable 

 for very gentle slopes or bar-trough profiles. Therefore, to model surf zone 

 energy dissipation, the more fundamental conservation of energy equation (44) 



dF 



-r^ + D = 

 dx 



where F is the general flux of energy toward the shore, D is ECgCosa, and 

 D, the local rate of energy dissipation per unit area, is preferred. Thus 

 local wave height in the surf zone is found by integration so that it depends 

 on all preceding seaward depths in addition to the local depth. The energy 

 balance equation can in principle be applied to bar-trough profiles, plus it 

 provides a convenient way to incorporate other energy loss mechanisms besides 

 wave breaking. 



Thornton (1976) listed the following mechanisms for dissipation of wave 

 energy in the surf zone: 



(1) Breaking induced internal turbulence forming rollers, vortices, 

 and eddies; 



(2) air entrainment requiring energy to lower air beneath the surface 

 and generation of more turbulence from rising air bubbles; 



(3) boiondary layer shear turbulence (bottom friction); 



(4) energy cascade to higher frequencies due to nonlinear transfer 

 processes and eventual dissipation as heat loss to surroundings; 



(5) percolation; and 



(6) work required to keep sediments in suspension and transport sedi- 

 ments . 



Recent theoretical attempts to use equation (44) in the development of wave 

 height distributions across the surf zone have concentrated on wave breaking 

 induced turbulence as the primary mechanism. 



Battjes (1978) estimated the dissipation rate per breaking wave from a 

 bore (moving hydraulic jump) of corresponding height. The broken wave height 

 was set equal to the water depth difference across the jump. The classic 

 hydraulic jump theory was modified to calculate the energy (head) loss rate 

 as an order of magnitude estimate. The results were incorporated in a model 

 of random waves and applied to plane and bar-trough profile beaches. Further 

 details are found in the Section VI of this chapter. Additional research 

 using hydraulic jump theory in the surf zone has been reported by Svendsen, 

 Madsen, and Hansen (1978a) and is continuing. 



Recently, Mizuguchi (1980) suggested another theoretical model for the 

 rate of energy dissipation in the surf zone. No physical explanation is of- 

 fered for its origin. The model contained a kinematic eddy viscosity 

 by Suhayda and Pettigrew (1977) confirmed these results. Thus the rate of 

 energy dissipation decreases with distance from the breaker line. 



Ill 



