Initial and boundary conditions 



40. An initial condition of rest was used in the wave-induced current 

 and setup model. Thus n , U , and V were zero at the start of the 

 calculations. Radiation stress gradients were then gradually built up to 

 their full values over a number of time-steps. The gradual buildup helped 

 avoid transients caused if the system were "shocked" by the sudden application 

 of radiation stress gradients. The solution was stopped when a steady state 

 was reached. Although the model has the capability to allow flooding of dry 

 land, wave setup was not great enough to cause flooding of the grid cells used 

 for Oregon Inlet. Thus along the shoreline a "no flow" (wall) condition was 

 assumed at the still-water line, and no flooding of the beach was allowed. 



For the lateral boundaries, a flux type boundary condition was used. That is, 

 the flux at a boundary cell was made equal to that at the next interior cell. 



41. On the offshore boundary, it is common practice to use conditions of 

 either "no flow" (wall) or constant elevation. However, both of these 

 conditions are highly reflective; and, as a result, the transients that 

 develop during the start-up of the numerical solution tend to bounce back and 

 forth between the offshore and nearshore boundaries and take a long time to 

 damp out. Figure 8 shows a typical transient developed for such a case. 

 These transients are evident in the results (Figure 9) presented by Ebersole 

 (1980). They produce significant problems in sediment transport models. For 

 example, for fixed wave conditions a steady state should develop such that 

 there is no on- or offshore movement of water along a straight coastline. If 

 transients are present that reflect between the coastline and the offshore 

 boundary, a steady condition of no flow in the on- or offshore direction is 

 not achieved. If steady state is assumed, cells will have small but steady 

 currents in on- and offshore directions that will produce steady erosion and 

 deposition. 



42. To eliminate the problem with transients, a radiation boundary con- 

 dition was used in the wave-induced current and setup model. This condition 

 allowed transients to propagate out of the computational grid. 



43. The radiation boundary condition was tested by considering a simple 

 plane beach. Ebersole (1980) noticed oscillations in the wave setup at the 

 beach (Figure 9), in the velocity in the offshore direction (Figure 10) and in 

 the longshore velocity (Figure 11). Considering similar wave conditions, the 

 model described in this report was run with the radiation boundary condition. 



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