Below is the ascii version of the abstract for 97-460.
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Numerical Simulation of Surface Water Waves on the Sphere
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.