In this example problem, we consider the propagation of long waves around a

circular island is simulated.

Homma (1950) and Jonsson, et al. (1976) showed that

extensive scattering occurs for long waves. This case tests and demonstrates the ability of

CGWAVE to handle strong scattering effects with a relaxed (Xu et al. 1996) boundary

condition. This boundary condition allows the model to be applied to a greater range of

modeling problems, as it does not require full reflection of the coastline outside the model

domain.

The modeled domain (Figure 22) consists of a circular island on a shoal with a

parabolic variation in depth. The island has a radius of 10 km. The open boundary is

placed at a radius of 35 km from the center of the island. The minimum water depth is

444 m at the edge of the island and increases to 4000 m at the outer edge of the shoal.

The domain has constant depth beyond the shoal. Incident wave periods of 240, 410 and

480 seconds are considered.

Figure 23 shows the results for the 240 second incident wave condition. This

figure has been divided in half due to symmetry of the solution. Waves are incident from

the left. The upper portion is the analytical solution, the lower portion is the CGWAVE

result. The CGWAVE results match the analytical solution. Notably absent are signs of

artificial boundary effects near the open boundary. Similar results were obtained for the

longer wave periods, with results matching the analytical data.

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