The nonlinear current profile theory of James (1973, 1974a) requires 

 further experimental verification. No application of cnoidal theory has 

 been attempted. The limited comparisons with James' data were all favor- 

 able suggesting that further work needs to be performed. Longuet-Higgins 

 (1972) stated the need to use nonlinear theory in Sj^y. 



Irregular wave theories of Battjes (1974a) and Goda (1975) need 

 experimental verification. Battjes' (1974a) inodel should be modified to 

 incorporate the Goda (1975) breaking criteria, the new Battjes and 

 Janssen (1976) surf zone model, and include lateral mixing stresses. The 

 available data should be curve fit to the theory at Vjjj to permit extraction 

 of closure coefficients as by Kraus and Sasaki (1979). It was surprising 

 to discover that additional theoretical effort with irregular waves has 

 not been pursued since the mid-1970's. The proven existence of harmonics 

 of the incident wave period in the surf zone and the detailed field test 

 results from the NSTS experiments are two good reasons for further theoret- 

 ical work with irregular waves. 



c. Closure Coefficients . Modified bottom shear-stress and lateral 

 mixing stress models were discussed in detail in Chapter 3 (See Tables 

 3 and 4). The more general expressions for xgy (e.g., eq. 80 by Bijker 

 and v.d. Graaff, 1978) ° for strong currents and large angles require 

 numerical solution techniques. Solutions for arbitrary variations of 

 bottom profile and roughness require numerical methods. The new surf 

 zone energy dissipation models require numerical integration. Also, 

 different models for lateral mixing stresses across the surf zone further 

 complicate the analysis. In short, all factors indicate that oversimpli- 

 fication to obtain analytic solutions is being abandoned in favor of more 

 general numerical solution techniques. Nonlinear and irregular wave 

 theories require such methods. 



The more general bed shear-stress formulations of Jonsson, Skovgaard, 

 and Jacobsen (1974) (eq. 76); Liu and Dalrymple (1978) (eq. 78 and others 

 not included); and Bijker and v.d. Graaff (1978)^6 (eq. 80) should be 

 considered further. In some cases, the closure coefficients for igy are 

 in themselves calculated from knowledge of the local bed roughness and 

 wave characteristics. This procedure is used in the Jonsson, Skovgaard, and 

 Jacobsen, and Bijker and v.d. Graaff models." It is preferred since it utilizes 

 more fundamental fluid mechanics stress coefficients based upon uniform 

 open channel flow and oscillatory water tunnel experiments. The Bijker 

 model especially warrants further study since it explicitly defines the 

 location above the bed where the velocity components are vectorially 

 combined. 



The more general lateral mixing stress models of Skovgaard, Jonsson, 

 and Olsen (1978) and Kraus and Sasaki (1979) (see Table 4) are preferred 

 since they separate the reduced mixing outside the surf zone. Both are 

 variations of earlier efforts and warrant further study. 



^^BIJKER and GRAAFF, op. ait. 



226 



