A potential enstrophy and energy conserving scheme for the shallow water equations
Abstract
To improve the simulation of nonlinear aspects of the flow over steep topography, a potential enstrophy and energy conserving scheme for the shallow water equations is derived. It is pointed out that a family of schemes can conserve total energy for general flow and potential enstrophy for flow with no mass flux divergence. The newly derived scheme is a unique member of this family, that conserves both potential enstrophy and energy for general flow. Comparison by means of numerical experiment with a scheme that conserves (potential) enstrophy for purely horizontal nondivergent flow demonstrated the considerable superiority of the newly derived potential enstrophy and energy conserving scheme, not only in suppressing a spurious energy cascade but also in determining the overall flow regime. The potential enstrophy and energy conserving scheme for a spherical grid is also presented.
- Publication:
-
Monthly Weather Review
- Pub Date:
- 1981
- DOI:
- 10.1175/1520-0493(1981)109<0018:APEAEC>2.0.CO;2
- Bibcode:
- 1981MWRv..109...18A
- Keywords:
-
- Atmospheric Circulation;
- Computational Fluid Dynamics;
- Energy Conservation;
- Finite Difference Theory;
- Orography;
- Potential Energy;
- Surface Roughness Effects;
- Flow Equations;
- Grids;
- Incompressible Flow;
- Lee Waves;
- Nonlinear Systems;
- Planetary Waves