b. Others . Hauguel (1980) employed a different numerical solution 

 strategy with the finite-difference method for equations (147) to (150). 

 A predictor-corrector scheme which uses the method of characteristics in 

 the prediction phase and a three time level implicit scheme in the corrector 

 phase is employed. Complete details are forthcoming since only the abstract 

 is presented in Hauguel (1980) . 



Additional efforts in one dimension iising the techniques developed by 

 Abbott, Petersen, and Skovgaard (1978a) for truncation error removal but 

 with an implicit three level box or Preissmann^^ scheme have been made by 

 McCowan (1978)°^ or are in progress by Jensen (personal communication, 1981). 



3. Simulation of Surf Zone Hydrodynamics . 



Research is currently in progress to extend the Boussinesq approach to 

 include wave breaking, surf zone energy dissipation, and lateral turbulent 

 mixing effects in an effort to simulate the hydrodynamics of the surf zone. 

 The main features of the flow are of interest which will be the instantaneous 

 depth- integrated velocity components and water depth. Time-averaging these 

 results would produce longshore currents, nearshore circulations, rip cur- 

 rents and MWL changes, if desired to compare with the many radiation stress 

 theories. Such numerical results are a few years in the future. 



In summary, the primary advantages of the Boussinesq approach are (a) 

 the insight into physical processes taking place within each wave period, 

 and (b) the elimination of the need to specify the wave height field by 

 other calculation procedures throughout the area of interest. On the other 

 hand, the approach still requires empirical surf zone simulations that are 

 just being developed plus large efficient computers for the extensive com- 

 putations. 



VIII. SUMMARY: THEORETICAL ASPECTS 



A comprehensive review and summary of relevant theories since 1967 has 

 been presented. The time-averaged radiation stress approach has been ex- 

 tended in considerable detail since first introduced. Mean water level 

 variations and net currents are linked together by the conservation laws of 

 mass and momentum. The primary driving force is created by the excess 

 momentum flux due to the waves, i.e. the radiation stress gradients. Major 

 modifications to the original theory have taken place primarily in three 

 areas : 



^^PREISSMANN, A., "PropagatiLo.n des Intumescenses Dans Les Canaux et Rivieres," 



Cer Congres de 1' Assoc. , Prancaise de Calcul, Grenoble, 1961, pp, 433-442 



(not in bibliography) . 

 ^^McCOWAN, A.D., "Numerical Slmultation of Shallow Water Waves," 4th Australian 



Conferenae on Coastal and Ocean Engineering ^ Adelaide, Nov. 1978, pp. 132-136 



(not in bibliography). 



155 



