The rate coefficient a controls the time rate of decay of the peak offshore 

 transport rate. 



327. Figure 40 displays the peak offshore transport rates from Case 300 

 and the least-squares fitted line according to Equation 20 (solid line). The 

 agreement Is very good and the regression equation explained over 90 percent 

 of the total variation. 



328. The average value of a was 0.91 hr"^, and the standard deviation 

 was 0.48 hr"''' for the 12 cases. To relate the decay coefficient to wave and 

 sand properties, a correlation analysis was carried out, although the data set 

 was small. The decay coefficient showed the strongest correlation to wave 

 period (r = 0.60) and the initial maximum transport rate (r = 0.65); that is, 

 a longer wave period or a larger initial peak offshore transport rate (profile 

 far from equilibrium shape) resulted in faster decay in the peak offshore 

 transport rate. Correlation with grain size (or fall speed) was very weak, 

 and no dependence on wave height could be found. Furthermore, it was not 

 possible to arrive at a regression equation with an acceptable coefficient of 

 determination by using any wave or sand parameters. 



329. Among the trial functions examined was also an exponential decay 

 with time, but this expression gave an Inferior fit compared to Equation 20, 

 especially at longer elapsed times , as there was a tendency for the peak 

 offshore transport rate to have a small but still significant value at the end 

 of a case. The exponential decay function approached zero too fast to 

 accurately reproduce this feature. Kajima et al . (1983a, b) developed a 

 conceptual model of beach profile change assuming that the peaks in the 

 transport rate distribution decayed exponentially with time. Sawaragi and 

 Deguchi (1981) also used an exponential decay to derive a time -dependent 

 transport relationship. 



330. An exponential decay is expected on general theoretical grounds, 

 since the response of the profile should be proportional to the departure from 

 equilibrium. However, microscale processes and, possibly, nonconstant forcing 

 conditions evidently alter the time decay to a more gradual approach to equi- 

 librium, causing a deviation of the profile response from the expected 

 exponential Idealization based on linear concepts. 



133 



