M.Sc Thesis
M.Sc Student Tobias Joshua A Simplified Approach to Tsunami Calculations Department of Civil and Environmental Engineering Professor Emeritus Michael Stiassnie

Abstract

The tsunami wave has been described on the basis of a simplified mathematical approach. The tsunamis are presented in two basic physical domains: in the region of the open sea; and in the vicinity of the continental shelf. The model discussed is of a tsunami generated outside the region of the continental shelf, and at a large distance from it, and in addition, propagates across the shelf, perpendicular to the shoreline.

The solution, presented on the basis of linear wave theory, originates from an initial displacement of the water free surface in the form of a cylindrical "Gaussian" located in the vicinity of the open ocean, defined by a cylindrical coordinate system with cylindrical symmetry. This analysis is related to the Cauchy- Poisson mathematical analysis and the solution presented in this work is given by Le Méhauté (1971).

The tsunami transforms as it passes from “deep” sea, over the continental slope, into the “shallow” continental shelf region, this calculated with the use of linear long wave theory.

Once the tsunami is on the sloping seabed of the continental shelf, the general solution is given with the use of the linear "shallow water" wave theory in a one dimensional coordinate system.

The final expressions for the tsunami in the open sea and continental shelf regions are given in the form of integral solutions and the results of this work are given after numerical integration of these expressions.

A wide range of results are presented for the region of the open sea and as a conclusion, the tsunami wave has been classified by two types of wave forms: the Wave- packet; and the Single- wave.

The analysis of different cases of tsunamis at the shoreline reveals that the continental shelf, due to its geometrical properties, serves as a tsunami amplifier, producing tsunami amplitudes up to 20 times larger than those at the edge of the continental shelf. The results also show that the damping factor, defined by two continental shelf parameters, i.e. the width of the shelf and the depth at its edge, has a substantial effect on resonance phenomena such as the wave amplitude amplification mentioned above, and the long duration of the wave fluctuation.

A comparison with historical tsunami measurements suggests that the simplified model may be used for a reliable assessment of the principle hydrodynamic properties of the tsunami, such as the tsunami amplitude and its half- period.