Publication Date:
2014-05-11
Description:
The shallow-water equations in spherical geometry are well known. They are derived as a constant-density, constant-gravity, specialisation of the hydrostatic primitive equations for a thin layer of fluid, bounded below by a topography, and above by a free surface. It is shown herein that it is possible to derive an analogous set of shallow-water equations in non-spherical (but zonally symmetric) geometry using orthogonal curvilinear coordinates. This equation set is dynamically consistent, possessing conservation principles for mass, axial angular momentum, energy, and potential vorticity. Furthermore, gravity is allowed to vary, as it does physically, as a function of latitude. This prepares the way to performing sensitivity tests, in an idealised framework, to assess the possible impact of latitudinal variation of gravity. Illustrative examples are given of models of gravity and of specific non-spherical coordinate systems.
Print ISSN:
0035-9009
Electronic ISSN:
1477-870X
Topics:
Geography
,
Physics
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