97-460 Panayotaros, P.

Numerical Simulation of Surface Water Waves on the Sphere (7890K, Tex) Aug 28, 97

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Abstract. We present a scheme for the numerical simulation of small amplitude water waves in spherical geometry. The method is based on a free-surface potential flow model of water waves. The equations of motion have a Hamiltonian structure, are non-local and we use them to derive simpler small amplitude wave equations for water of arbitrary depth. In our simulation we consider such equations, and our numerical implementation preserves the Hamiltonian structure of the evolution. This fact is used to test the accuracy of the numerical integration and also in understanding some of the qualitative properties of small amplitude solutions. In particular, our observations suggest that the numerical solutions of the approximate equations are very accurate and that small solutions remain bounded.

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