Abstract
We develop a variational integrator for the shallow-water equations on a
rotating sphere. The variational integrator is built around a discretization of
the continuous Euler-Poincar\'{e} reduction framework for Eulerian
hydrodynamics. We describe the discretization of the continuous
Euler-Poincar\'{e} equations on arbitrary simplicial meshes. Standard numerical
tests are carried out to verify the accuracy and the excellent conservational
properties of the discrete variational integrator.