A New Fourth-Order Enstrophy and Energy Conserving Scheme

Abstract

A new pseudo-fourth-order finite-difference scheme for the shallow-water and primitive equations is derived. This scheme is a C-grid scheme that conserves energy and conserves enstrophy in the nondivergent limit. The accuracy of the scheme is second order, but in the nondivergent limit it has fourth-order accuracy. In the nondivergent limit, the scheme reduces to Arakawa's fourth-order Jacobian scheme for the vorticity equation for two-dimensional incompressible flow. Model runs with the shallow-water equations are discussed.