A potential enstrophy and energy conserving scheme for the shallow-water equations extended to generalized curvilinear coordinates

This is an extension of a scheme formulated by Arakawa and Lamb for orthogonal coordinate systems. The starting point for the present scheme is the shallow-water equations cast in generalized curvilinear coordinates, and tensor analysis is used to derive the invariant conservation properties.

Preliminary tests on a flat plane with doubly periodic boundary conditions are presented. The scheme is shown to possess similar order-of-convergence error characteristics using a non-orthogonal coordinate compared to Cartesian coordinates for a nonlinear test of flow over an isolated mountain. A linear normal mode analysis shows that the discrete form of the Coriolis term provides stationary geostrophically balanced modes for the nonorthogonal coordinate and no unphysical computational modes are introduced.