The small vertical mark on these profiles Indicates approximately where 

 maximum wave setdown occurs, as determined from Figure 40. This would be 

 the location of the breaker line in the periodic theory. The extent and 

 magnitudes of the longshore currents outside this breaker line are more 

 realistic (than Collins, 1972) in that the current drops off rapidly. 



Figure 42(b), the solijd lines, shows the influence of wave steepness 



for narrow spectra when a = 15° (y = 0.8). Steeper wave decrease both 



the width and magnitude of the longshore current. This is because mean 



value length is included in the breaking criterion and long waves create a 



wider surf zone for a given H . 



o 



The dashline in Figure 42(b) is the longshore current profile for a 

 broad spectrum of the Pierson-Moskowitz type and a cos^a-type spreading. 

 Battjes (1972, 1974a) derived the theoretical expressions for radiation 

 stresses in short-crested waves in deep water to prove that, in general, 

 short-crestedness reduces all the radiation stress components. In shallow 

 water, S is 50 percent smaller for short-crested waves and a cos^a-type 

 spreading of the directional spectrum. This result manifests itself in 

 roughly the same percentage reduction in longshore current magnitude as il- 

 lustrated by this one example in Figure 42(b). After further study of the 

 complicated relationships between short-crested radiation stresses, bottom 

 shear stress, and longshore currents, Battjes (1974a), in fact, concluded 

 that 



"...for the purpose of longshore (current) calculations. . .the 

 wave energy can be lumped into a very narrow frequency-and- 

 direction interval (and)... the velocities so obtained are 

 afterwards reduced by a factor equal to the ratio of the deep- 

 water radiation shear stresses corresponding to the actual 

 spectrum and the lumped, narrow spectrum." (p. 151) 



This procedure eliminated the need to carry out a number of numerical inte- 

 grations over the two-directional broad band spectrum. 



It is not clear why additional theoretical work with irregular waves 

 has not been pursued since 1974. The effects of more realistic strong cur- 

 rent large-angle bed stress models, inclusion of lateral mixing stress terms, 

 and incorporation of more sophisticated energy dissipation models for the 

 surf zone would all be extremely interesting modifications. Perhaps with 

 the recent availability of detailed field test results from the NSTS experi- 

 ments to use as comparison, such computations are now warranted. Two- 

 dimensional circulation and rip current computations for irregular waves 

 have yet to be attempted. 



VII. BOUSSINESQ METHODS 



The time-averaged approach using radiation stress theory is the funda- 

 mental basis behind the theoretical results summarized in Sections II to 

 VI. It has become the accepted theory of coastal hydrodynamics. 



144 



