Of interest here are the equations obtained when both wave and random 

 turbulent fluctuations are present together. The derivation is quite 

 lengthy and involves further simplifications and assumptions. The resulting 

 horizontal motion equations are almost identical to equations (108) and (109), 

 except as follows: 



(1) At the true scales of random turbulence, additional Reynolds stress 

 terms appear, 



(2) the component of effective stress due to the deviation of the local 

 velocity from its depth-averaged value appears as a separate stress 

 component, 



(3) the lateral stress terms due solely to wave scale interactions with 

 the traditional radiation stresses, and 



(4) a number of additional new interaction stress terms appear that have 

 never been studied in detail before. 



All these new stress terms are proportional to the square of the wave ampli- 

 tude. Harris and Bodine (1977) postulated that all these terms are generally 

 smaller than the radiation stresses and can generally be neglected because of 

 uncertainties in the radiation and turbulence stresses. No reasons are given. 

 It will undoubtedly prove necessary to lump these additional interaction 

 stresses (4) with the others until vastly improved data are available. Those 

 due to vertical velocity profile variations (2) could become important within 

 and near rip currents and could be incorporated as momentum correction factors 

 (g) in the convection terms. The bed friction and lateral eddy viscosity will 

 continue to serve as closvire coefficients to absorb these unknown stresses. 



The question of form of conservation equations for waves in the surf 

 zone including turbulence is an active research area (e.g., see Madsen and 

 Svendsen, 1978). But in all cases, the solution first requires the a priori 

 specification of the wave height field to evaluate the radiation stress gra- 

 dients. 



2. Specification of Wave Height Fields . 



The wave heights outside and within the surf zone must be known before a 

 solution of the mass and motion equations can begin. This is implied in all 

 time-averaged methods using radiation stress gradients where the local wave 

 heights appear in the total energy density, E. In addition, wave orbital 

 velocities needed in the bottom shear-stress terms require local wave height 

 information. For this purpose, standard wave refraction, diffraction, and 

 reflection computation procedures are normally employed outside the breaker 

 line. Within the surf zone wave height variations in space are found using 

 the surf zone empirical relations discussed above. For complicated beach pro- 

 files with bar-trough bathymetry and near groins, offshore breakwaters, or 

 other structures, the detailed specification of the wave height fields through- 

 out the entire nearshore zone of interest can be a tedious and difficult task. 

 Many numerical computation systems are available for this purpose (e.g., see 

 Noda 1972a, 1974) or have been specially adapted for use with nearshore cir- 

 culation solution techniques (e.g., Liu and Mei, 1975). All the systems have 

 limitations and special problems that develop at caustics with soliton forma- 

 tion and are usually based only on linear wave theory. In addition, percola- 

 tion, bottom friction, and, most importantly, current-refraction effects on 

 the specified wave height fields are usually neglected. 



119 



