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A Potential Enstrophy and Energy Conserving Numerical Scheme for Solution of the Shallow-Water Equations on a Geodesic Grid

A Potential Enstrophy and Energy Conserving Numerical Scheme for Solution of the Shallow-Water... Using the shallow water equations, a numerical framework on a spherical geodesic grid that conserves domain-integrated mass, potential vorticity, potential enstrophy, and total energy is developed. The numerical scheme is equally applicable to hexagonal grids on a plane and to spherical geodesic grids. This new numerical scheme is compared to its predecessor and it is shown that the new scheme does considerably better in conserving potential enstrophy and energy. Furthermore, in a simulation of geostrophic turbulence, the new numerical scheme produces energy and enstrophy spectra with slopes of approximately K −3 and K −1 , respectively, where K is the total wavenumber. These slopes are in agreement with theoretical predictions. This work also exhibits a discrete momentum equation that is compatible with the Z-grid vorticity-divergence equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monthly Weather Review American Meteorological Society

A Potential Enstrophy and Energy Conserving Numerical Scheme for Solution of the Shallow-Water Equations on a Geodesic Grid

Monthly Weather Review , Volume 130 (5) – Apr 9, 2001

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References (19)

Publisher
American Meteorological Society
Copyright
Copyright © 2001 American Meteorological Society
ISSN
1520-0493
DOI
10.1175/1520-0493(2002)130<1397:APEAEC>2.0.CO;2
Publisher site
See Article on Publisher Site

Abstract

Using the shallow water equations, a numerical framework on a spherical geodesic grid that conserves domain-integrated mass, potential vorticity, potential enstrophy, and total energy is developed. The numerical scheme is equally applicable to hexagonal grids on a plane and to spherical geodesic grids. This new numerical scheme is compared to its predecessor and it is shown that the new scheme does considerably better in conserving potential enstrophy and energy. Furthermore, in a simulation of geostrophic turbulence, the new numerical scheme produces energy and enstrophy spectra with slopes of approximately K −3 and K −1 , respectively, where K is the total wavenumber. These slopes are in agreement with theoretical predictions. This work also exhibits a discrete momentum equation that is compatible with the Z-grid vorticity-divergence equation.

Journal

Monthly Weather ReviewAmerican Meteorological Society

Published: Apr 9, 2001

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