A new approach which employs the Boussinesq equations of motion that 

 are depth- integrated but not time-averaged is emerging. Vertical accelera- 

 tions resulting from streamline curvature of swell-type wind waves (periods 

 down to 6 seconds) create a nonhydrostatic pressure distribution. Additional 

 terms appear in the real-time motion equations that effectively account for 

 the excess horizontal momentum flux in much the same way as the radiation 

 stress terms. These terms are higher order differentials of the dependent 

 variables (velocity and depth) so that equation solution determines the in- 

 stantaneous currents and water surface variations as the waves propagate near 

 the coast. Wave shoaling, refraction, diffraction, reflection, and current 

 interactions are automatically part of the solution. 



The theory can adequately describe nonlinear, nonpermanent form wave 

 propagation over variable bathymetry to near the breaking limit. The equa- 

 tions required and some initial engineering applications outside the breaker 

 zone are described below. Research and development is currently taking 

 place to extend the theory to include wave breaking and energy dissipation 

 in the surf zone. The instantaneous currents and water surf variations that 

 result could then be time-averaged if it was desired to compute mean long- 

 shore currents, circulations, and setup. However, because of the highly 

 nonlinear response of sediment to near-bottom velocities, the direct use of 

 the instantaneous results coupled with sediment transport equations is ex- 

 pected. 



The present situation is roughly analogous to tidal hydraulic and mass 

 transport understanding in estuaries in the 1950' s. The motion equation was 

 time-averged over the tidal period to present a view of the net velocity 

 distribution and circulations in the estuary. Much effort went into re- 

 formation of bed shear, turbulence dispersion, and sediment transport based 

 on the time-averaged flows. The entire approach was abandoned when the 

 numerical computation of the exact unsteady-flow equations became economical 

 and realistic on the computer. This has subsequently led to much clearer 

 understanding of mass, momentum, and energy transport processes for unsteady 

 river and estuarine flows. 



The ratio of tide-to-wind wave period is about 5000:1. Although signif- 

 icant improvements in size and speeds of computers continue, the simple fact 

 remains that vast numbers of grid points and time steps are needed to ac- 

 curately resolve wind waves in the coastal zone. Real time methods will re- 

 main a research tool for the near future. 



1. Boussinesq Theory . 



The theory that incorporates vertical accelerations, to a limited ex- 

 tent, in the horizontal motion equations is called Boussinesq theory 

 (Boussinesq, 1872) . Many forms of the equations attributable to Boussinesq 

 are found in the literature and are possible due to the order of accuracy 

 of terms retained and methods of derivation. They will still be referred 

 to as Boussinesq equations or theory. Simplification of the equations by 

 limiting wave propagation to one direction (no reflections) gives the 



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