so that comparing equations (43) and (25) gives 



S =^^Y^ (45) 



xy c X 



where sina/c is also constant due to Snell's law. Longuet-Higgins (1972) 

 proved that equation (45) is independent of the wave theory involved. Conse- 

 quently, the driving force in the y-direction momentum balance equation (42) 

 for longshore current becomes 



dS . dF^ . . 



xy sina X /Sina.„ ,,,, 



J ■ ' = J — = -( )D (46) 



dx c dx c 



and is thus directly proportional to the energy dissipation. "If there were 

 no dissipation, there would be no current" (Longuet-Higgins, 1972). 



Outside the breakers, if the energy flux is assumed constant, no energy 

 is dissipated (D = 0) and consequently the longshore current must be identi- 

 cally zero. Inside the surf zone, continuous spilling-type breakers dissipate 

 large amounts of wave energy to generate a longshore current. F^^ is needed to 

 be a continuous function of x in the surf zone to validate equation (44) . 

 Longuet-Higgins (1972) argued that most of the energy dissipation is due to 

 wave breaking and not due to the bottom shear stresses. Thus, the shape of 

 the wave height decay curve in the surf zone, as shown in Figure 23 and em- 

 pirically determined from the breaker ratio, Y> plays a key role in the theo- 

 retical longshore current profile. Wave breaking, internal turbulent shears, 

 and resulting energy dissipation as heat loss to the surroundings are the main 

 mechanism driving the longshore current. 



From the point of view of the momentum balance equation (42) , the common 

 belief is that the bottom shear stress dictates the strength of the longshore 

 current. The lateral turbulent stresses only redistribute or smooth the velo- 

 city normal to the shore (e.g., see Horiwaka, 1978, p. 210). The question of 

 the relative importance of internal turbulence dissipation and bottom shear 

 is discussed further by examining their relative magnitude in the theoretical 

 equations. 



2. Original Model . 



The use of radiation stress principles in the development of a theory 

 for uniform longshore current profiles was first made by Bowen (1969a) , 

 Thornton (1969), Bakker (1970)^5, iwata (1970), and Longuet-Higgins (1970). 

 All used a longshore momentum balance as equation (42) but with some differ- 

 ences in the formulations for the three terms involved. Here the model by 

 Longuet-Higgins (1970) has been designated as the original model primarily 



^^BAKKER, W.T., "Littoral Drift in the Surf Zone," Study Rept. WWK70-16, 

 Directorate for Water Management and Hydraulic Research, Coastal Research 

 Department Rijkswaterstaat , The Hague, The Netherlands, 1970 (not in bibliog- , 

 raphy) . 



82 



