Panayotaros, P.
Numerical Simulation of Surface Water Waves on the Sphere
(7890K, Tex)

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.