4. General One-line Shoreline Model (Price, Tomlinson, and Willis, l^/^i . 



Price, Tomlinson, and Willis' formulation consists of the sediment 

 continuity equation and the total sediment transport equation 



0.70 E, (nC). sina, cosa. 



^S Y (1 - p) ' (S^ - 1) (^^ 



u S V 



in which E represents the wave energy density, (nC) the group velocity, 

 a the angle between the breaking wave front and the shoreline, y^ the 

 specific weight of water, p the in-place sediment porosity, and Sj the 

 specific gravity of the sediment relative to the water in which it is 

 immersed. The subscript "b" represents values at breaking. 



Two formulations were presented by Price, Tomlimson, and Willis (1972). 

 In the first. Equation (7) was substituted into the continuity equation and 

 the results cast into a finite-difference form. In the second, the two 

 equations were employed separately. The latter formulation was selected due 

 to its simplicity and used for the results presented. 



Computations were carried out for the case of beach response due to the 

 placement of a long impermeable barrier. The total sediment transport 

 equation by Komar (1969) was used and the planform was calculated at 

 successive times. Refraction was apparently not accounted for in the 

 numerical model. To verify the computations, a physical model study was 

 carried out for the same conditions using crushed coal as the modeling 

 material. The comparison was interpreted as good for up to 3 hours; however, 

 for greater times, substantial differences occurred and these were inter- 

 preted as being due to wave refraction not being represented. The crushed 

 coal was supplied to the model at the updrift end at a rate based on the 

 Komar equation, and the results were interpreted as substantiating this 

 relationship. However, the updrift end of the model beach receded SLibstan- 

 tially both in the numerical and physical models. In the physical model, 

 this can only be interpreted as due to the Komar equation predicitions being 

 less than the actual transport rate, possibly due to the low specific gravity 

 (1.35) of the crushed coal. The predicted recession of the updrift beach is 

 puzzling, although it could be due to a problem in properly representing the 

 updrift boundary condition. 



Other one-line models for shoreline changes in the vicinity of coastal 

 structures were developed by LeMehaute and Soldate (1977) and Perl in (1978). 

 Perlin also developed a two-line model formulation, with one-line represent- 

 ing the shoreline and the second the offshore. Dragos (1981) developed an 

 n-line nodel for bathymetric changes due to the presence of a littoral 

 barrier. 



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