height, and angle at the shoreline. The original model of Longuet-Higgins (1970), 

 modified by U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 

 (1977)^^ is then used to calculate a mean longshore current. Although local winds 

 are a dominant feature of the field data displayed, no term to include surface 

 wind shear-generated currents is included. 



e. Others Outside the United States . In Japan, Sasaki (1977) essen- 

 tially followed the efforts of Noda, et al. (1974) and neglected all the 

 terms in the basic equations except mean water surface gradient, radiation 

 stress gradient, and bottom shear. The weak current small-angle friction 

 model is employed. The wave height field is calculated numerically but 

 neglects wave-current interactions. A successive overrelaxation (SOR) nu- 

 merical method solved the resulting equations after first being put in 

 transport stream-function form. Because of the large number of omitted terms 

 and neglect of wave setup, the model is only valuable as a general indicator 

 of trends (see Ch. 4). 



In response to the need to investigate currents near a proposed cooling 

 water intake basin on the coast, Bettess, et al. (1978), in England, de- 

 veloped a steady-state finite-element model. It included all terms in the 

 motion equations plus the Coriolis accelerations. Wave-current refraction 

 effects in the wave height field calculations were neglected. Wave height 

 fields were also calculated using the finite-element method for solution of 

 Berkhoff's (1972)^^ modified form of the shallow-water equations. An example 

 of their results for currents calculated using a constant eddy viscosity co- 

 efficient is shown as Figure 36. The size and strength of the large eddy in 

 the lee of the breakwater compares favorably with physical model results 

 (dotted lines). The authors call for an improved means to simulate surf zone 

 energy decay, radiation stresses with standing waves, and lateral mixing 

 eddy coefficients in order to improve the numerical simulation. 



Finally, Vreugdenhil (1980) carefully outlines methods presently being 

 implemented at the Delft Hydraulics Laboratory to develop a numerical model 

 for unsteady wave-driven currents. The primary purpose of this model is to 

 better understand physical processes such as migrating rip currents. The 

 equations employed are written in conservation form (eqs. 107, 108, and 109) 

 with all terms included. Modules are introduced to permit easy variation or 

 suppression of submodels for lateral mixing stress, bottom friction, the 

 wave theory in the radiation stress, wave breaking, and the surf zone energy 

 loss criteria. Wave height fields are computed from linear theory to include 

 refraction from both depth and current variations, and diffraction effects 

 can also be included. 



The ntmierical method selected as the finite-difference method of the 

 implicit type. Together with a transformed coordinate system to readily 

 handle curved breaker lines and boundaries, the finite-difference method 

 was felt superior to the finite-element method where little is known about 



3^U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore 

 Proteotian Manual, Vol. I, U.S. Government Printing Office, Washington, D.C., 

 1977 (not in bibliography) . 



^^BERKHOFF, J.C.W., "Computation of Combined Diffraction-Refraction," Froceed- 

 ings of the 13th Coastal Engineering Conference ^Vancouver , 1972 (not in bibliog- 

 raphy) . 



129 



