flow rate, width or size, and surprisingly there are little field data 

 to compare with numerical simulations. 



Finally, for near-normal wave incidence, vertical gradients in the 

 velocity fields can create vertical radiation stress gradients to drive 

 circulations about the horizontal axis. No attempts were uncovered to 

 apply radiation stress theory to this case for estimates of circulation 

 currents schematized in Figure 22, 



e. Boussinesq Theory . Research has' essentially just begun. Out- 

 side the surf zone, numerical shoaling results compare very favorably 

 with experiments. More research and comparisons are necessary near the 

 breaking limit. Only one comparison of two-dimensional wave transforma- 

 tions against physical laboratory measurements has been published in 

 the literature (Fig. 86). Much more evidence is desired. 



The correct form of the Boussinesq equations for variable bathy- 

 metry has yet to be determined. No wave breaking, surf zone, wave setup, 

 or longshore current simulations have been reported in the literature. 



Great care is required in the numerical methods to ensure accuracy 

 in wave amplitude and phase propagation. Large and high-speed computers 

 are necssary. For these reasons, future developments will remain for 

 research purposes rather than engineering applications. 



The analogy, with time-averaged tidal hydraulics analyses of the 

 1950 's was cited earlier. The digital computer permitted calculations 

 within each tidal period to enhance knowledge. Guza and Thornton (1978) 

 in their article on time variability of longshore currents make a similar 

 comment. In the 1950 's, large-scale ocean circulations were thought 

 to be driven by average winds to produce generally weak and horizontally 

 smooth currents. The relative importance of drag and eddy diffusivity 

 terms was discussed, as we have summarized in this report. Nonlinear 

 terms were then needed to explain the jetlike Gulf Stream; as their 

 importance in rip current dynamics is now recognized. Still later, instan- 

 taneous measurements showed large temporal and spatial fluctuations, 

 in contrast to observations with floats that matched the theory for 

 yearly means . Large cooperative experiments were then conducted in an 

 effort to determine the importance of the shorter scale fluctuations 

 on the longer scale flows. These final questions remain unresolved. 

 Considering the gross nonlinearity of the surf zone and the strong 

 analogy cited with oceanic research, Guza and Thornton (1978) concluded 

 that it is overly optimistic to expect simple solutions to mean nearshore 

 flows. 



The Boussinesq theory does offer some possibilities in this regard 

 by going beyond the time-averaged mean to look within each wave period 

 at the physics taking place. 



229 



