## Abstract

The finite-element, semi-implicit, and semi-Lagrangian methods are combined together to solve the shallow-water equations using unstructured triangular meshes. Triangular finite elements are attractive for ocean modeling because of their flexibility for representing irregular boundaries and for local mesh refinement. A kriging interpolator is used for the semi-Lagrangian advection, leading to an accurate representation of the slow Rossby modes. The terms that govern fast gravitational oscillations are discretized using the semi-implicit scheme, thereby circumventing a severe time step restriction. A low-order velocity–surface-elevation finite-element basis-function pair is used for the spatial discretization. Results of test problems to simulate slowly propagating Rossby modes illustrate the promise of the proposed approach for ocean modeling.

* Current affiliation: National Center for Atmospheric Research, Advanced Study Program, Boulder, Colorado.

^{+}Current affiliation: U.K. Meteorological Office, Bracknell, Berkshire, United Kingdom.

*Corresponding author address:* Dr. Daniel Y. Le Roux, Dept. of Atmospheric and Oceanic Sciences, McGill University, Centre for Climate and Global Change Research, Montreal PQ H3A 2K6, Canada.

Email: dleroux@cerca.umontreal.ca