4. Sand Transport Model . 



a. Governing Equations . Three basic equations are used to simulate the 

 sediment transport and bathymetry changes according to the wave field. The 

 equation of continuity 



3q aq 

 ^ + ^ + ^ = (20) 



3t 3x ay 



requires as input, knowledge of the longshore and cross-shore components of 

 sediment transport. The total transport alongshore has been measured by 

 several investigators and many equations exist; however, the distribution of 

 the transport across the surf zone is not well known. Fulford (1982) based 

 on laboratory data from Savage (1959), developed a distribution of longshore 

 sediment transport across the surf zone for the case of straight and parallel 

 contours. Ful ford's use of Savages experiment v/as based on two assumptions: 

 1) the structure must be a total littoral barrier and 2) onshore-offshore 

 sediment transport could be neglected. Test 5-57 was chosen because the two 

 criteria were nearly met. Savage reported that the groin acted as a total 

 littoral barrier for the first 35 hours of the test (i.e., no bypassing 

 occurred prior to 35 hours). This does not mean that no onshore-offshore 

 transport occurred because as the profile steepens on the updrift side, 

 onshore-offshore transport does occur. However, it was assumed to be 

 negligible. In addition, the initial profile had been molded to an 

 equilibrium profile via 150 hours of waves. Thus, the two criteria required 

 to develop an inferred longshore distribution of sediment transport were 

 nearly satisfied. This distribution is shown as a dashline in Figure 4. The 

 smaller "maximum" is believed to be an extraneous effect of a groin downdrift 

 from the location in the experiment where the data were taken. Therefore, 

 this feature was replaced by a monotonically decreasing, smooth curve as 

 shown by the "altered" curve. To analytically represent this distribution, a 

 function of the following form was chosen 



q^ (y) = (B) (y)""^ e"^^^ (21) 



This type of equation is convenient because it is easily integrable, and by 

 properly choosing the constant, B, the integral of the equation from zero to 

 infinity can be required to equal a particular value. This too is highly 

 desirable because, as was done in the model, the integral is set equal to one 

 and then multiplying by the value of the well -known longshore transport 

 equation, the value of the transport at any location across the surf zone can 

 be determined. Further investigation suggested a value of n = 3 to produce a 

 curve similar to Fulford's curve. A more general form of the equation which 

 allows more flexibility and curve fitting is 



mt 



q^(y) = B(y + a)2 e^ I'o^TU (22) 



