Article Type:
Research Article

The Deep-Atmosphere Euler Equations in a Generalized Vertical Coordinate

Andrew Staniforth Met Office, Bracknell, United Kingdom

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Nigel Wood Met Office, Bracknell, United Kingdom

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Print Publication:
01 Aug 2003
DOI:
https://doi.org/10.1175//2564.1
Page(s):
1931–1938
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Abstract

Previous analysis of the hydrostatic primitive equations using a generalized vertical coordinate is extended to the deep-atmosphere nonhydrostatic Euler equations, and some special vertical coordinates of interest are noted. Energy and axial angular momentum budgets are also derived. This would facilitate the development of conserving finite-difference schemes for deep-atmosphere models. It is found that the implied principles of energy and axial angular momentum conservation depend on the form of the upper boundary. In particular, for a modeled atmosphere of finite extent, global energy conservation is only obtained for a rigid lid, fixed in space and time. To additionally conserve global axial angular momentum, the height of the lid cannot vary with longitude.

Corresponding author address: Dr. Andrew Staniforth, Met Office, Room 249, London Road, Bracknell RG12 2SZ, United Kingdom. Email: Andrew.Staniforth@metoffice.com

Abstract

Previous analysis of the hydrostatic primitive equations using a generalized vertical coordinate is extended to the deep-atmosphere nonhydrostatic Euler equations, and some special vertical coordinates of interest are noted. Energy and axial angular momentum budgets are also derived. This would facilitate the development of conserving finite-difference schemes for deep-atmosphere models. It is found that the implied principles of energy and axial angular momentum conservation depend on the form of the upper boundary. In particular, for a modeled atmosphere of finite extent, global energy conservation is only obtained for a rigid lid, fixed in space and time. To additionally conserve global axial angular momentum, the height of the lid cannot vary with longitude.

Corresponding author address: Dr. Andrew Staniforth, Met Office, Room 249, London Road, Bracknell RG12 2SZ, United Kingdom. Email: Andrew.Staniforth@metoffice.com

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