A three-dimensional generalization of Eliassen's balanced vortex equations derived from Hamilton's principle
✍ Scribed by George C. Craig
- Publisher
- John Wiley and Sons
- Year
- 1991
- Tongue
- English
- Weight
- 713 KB
- Volume
- 117
- Category
- Article
- ISSN
- 0035-9009
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✦ Synopsis
Abstract
A new set of equations is derived for nearly circular flow in gradient balance. For precisely axisymmetric motion, the system reduces to the well‐known balanced vortex equations of Eliassen. The derivation is based on the assumption that the radial component of velocity is small in comparison to the azimuthal component. By applying this approximation to Hamilton's principle for a continuum of fluid parcels, while preserving the time and particle‐labelling symmetries of the primitive equations, it is ensured that the resulting system possesses conservation laws for energy and potential vorticity. In potential radius coordinates, the Lagrangian equations of motion take the form of the geostrophic and hydrostatic balance conditions. The system is also presented in Eulerian form, and a practical integration scheme, based on a linear elliptic equation for geopotential tendency, is described. Finally, the set is rederived by a conventional scale analysis in order to determine constraints on the diabatic forcings which are required for consistency with the approximation.