pass over the main bar and break inshore, causing deposition of sand shoreward 

 of the bar. The flat portion of the bar was a result of waves breaking 

 shoreward of the bar crest. The seaward peak of the bar was created from 

 waves breaking at the bar crest when water level was at a minimum. 



469. Somewhat similar profile development occurred when wave height was 

 varied sinusoidally . As an example, deepwater wave height was varied between 

 1 and 3 m, with the wave period fixed at 10.0 sec and the water level con- 

 stant. In Figure 73, selected profiles predicted by the model are displayed 

 at consecutive times, together with the calculated wave height distribution at 

 the last time-step. The bar had a flat shape initially, but a pronounced peak 

 formed after a number of wave height cycles had been completed. 



470. The constant supply of sand from the dune as the wave height 

 changed, together with the movement of the break point, prevented the inshore 

 from developing a characteristic monotonic shape. However, if the wave height 

 is held constant, the beach profile would approach an equilibrium shape with a 

 concave inshore profile. 



471. As an example of the shape of the net cross-shore transport rate, 

 distributions associated with Figure 73 are plotted in Figure 74. The peak of 

 the transport rate distribution moved across -shore with movement of the break 

 point as wave height varied. At some time -steps, a small peak appeared at the 

 foreshore (not shown in Figure 74, but seen in Figure 58), particularly if 

 avalanching took place on the dune slope. In this case, sand accumulated in 

 the foreshore cells as the slope adjusted to the residual angle after shear- 

 ing. The corresponding decrease in depth produced a larger energy dissipation 

 per unit volume in those cells, resulting in a greater transport rate. Figure 

 74 also shows that the transport rate distribution exhibited a more complex 

 shape at later times, when the depth was not monotonically decreasing. 



472. A hypothetical case was also numerically simulated for concurrent 

 sinusoidal variations of water level (±1 m) and wave height (2 m ±1 m) . 

 Variation of the two parameters was in phase with a period of 200 time -steps 

 (At = 5 min) . The total simulation time was 1,000 time -steps, and the wave 

 period was 8 sec. As seen from Figure 75, the bar is higher and wider than in 

 previous examples. Also, the dune face retreated more than for the example 

 with only wave height variation, since the waves could attack higher on the 

 dune because of the water level variation 



197 



