A Numerical Study Of The Tsunami Response Of The Hawaiian Islands

The response of linearized long waves to the eight major Hawaiian Islands is investigated numerically using a mathematical model of the island system. A spline interpolation scheme is utilized to convert the actual soundings of the island bathymetry to a 5.5 km square grid closely approximating the topography of the islands. A time-marching, central difference, explicit scheme is used to evaluate the wave field by the linear, long wave, Eulerian equations of motion and continuity in Cartesian coordinates for a frictionless, homogeneous fluid. The condition of no normal flow is employed at the island shorelines and a localized interpolation technique is utilized at the outer boundary to simulate a free-flow boundary. Verification of the numerical procedure is accomplished by agreement with analytic solutions of steady-state problems involving wave interaction with geometric islands in both constant and variable depth cases. Island response is determined by using a generalized time sequence input with a stipulated spectrum in the tsunami frequency range. This input is time stepped through the model for a duration sufficient to establish a statistical equilibrium within the system. The shoreline hydrographs, which record the time history of water elevation around the islands, are Fourier analyzed to obtain spectra for each shoreline point. These spectra are divided by the input spectrum to obtain transfer functions which represent the relative response of the system to waves in the tsunami period range. Verification of the response analysis is judged in terms of the agreement with the analytic response of a variable depth geometric island to a set of tsunami period waves. A technique for determining the period cutoff of a particular model system is demonstrated by comparison of responses of the same model using coarse and fine grids. The response analysis methods are applied to the model of the Hawaiian Islands for the case of a tsunami originating in the Alaskan region. Transfer functions are shown in averaged and contoured form for the island system and each individual island. The model study reveals that the numerical technique is appropriate for the response study of the Hawaiian Islands, that there are at least nine characteristic periods in the tsunami range to which the islands respond, and that interinsular reflections generate areas of high energy concentrations.