Harbour Resonance: Comparison with the Analytical solution given by Ijima

Contours of normalized wave height in the rectangular harbour.

The displayed contours are the responses near peak harbour resonance.

Ijima et al. (1981) gave the analytical solution of this rectangular harbor with a harbor length = 2h, harbor width = h, a constant water depth outside the harbor (h = 0.1 m), and a constant slope within the harbor. On the left side of this computing domain, the given boundary condition was specified.  Along the harbor perimeter, the total reflection B.C. ( = 0) was specified.  At the top and bottom open boundaries, the total passing through B.C. was assigned ( = 1).  The incident wave height is given as H_i.  When the ratio of harbor length to wave length approaches 1/4 (kh 1.2), the ratio of H_e/H_i reaches 8 and demonstrates the first resonance; the second resonance occurred at kh 3.7.  Because an approximation (i.e., the rectangular open boundary) of the exact geometry for the open boundary was used, the model-calculated resonance responses are not as accurate as the analytical solutions.  As pointed out by Chen (personnel communication 1997), a semi-circle open boundary is needed for an accurate simulation of the resonance.  The calculated contours of the normalized wave height at a near resonance frequency  further demonstrate that the scatter waves propagated outward from the harbor entrance and showed why a semi-circular open boundary is needed. For details, see Maa and Hwung (1998).

Comparison of the model calculated wave height at the harbour end with the analytical solution.