Unsteady analytical solutions of the spherical shallow water equations
A new class of unsteady analytical solutions of the spherical shallow water equations (SSWE) is presented. Analytical solutions of the SSWE are fundamental for the validation of barotropic atmospheric models. To date, only steady-state analytical solutions are known from the literature. The unsteady...
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| Veröffentlicht in: | Journal of computational physics 2005-12, Vol.210 (2), p.535-553 |
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| container_title | Journal of computational physics |
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| creator | Läuter, Matthias Handorf, Dörthe Dethloff, Klaus |
| description | A new class of unsteady analytical solutions of the spherical shallow water equations (SSWE) is presented. Analytical solutions of the SSWE are fundamental for the validation of barotropic atmospheric models. To date, only steady-state analytical solutions are known from the literature. The unsteady analytical solutions of the SSWE are derived by applying the transformation method to the transition from a fixed cartesian to a rotating coordinate system. Fundamental examples of the new unsteady analytical solutions are presented for specific wind profiles. With the presented unsteady analytical solutions one can provide a measure of the numerical convergence in the case of a temporally evolving system. An application to the atmospheric model PLASMA shows the benefit of unsteady analytical solutions for the quantification of convergence properties. |
| doi_str_mv | 10.1016/j.jcp.2005.04.022 |
| format | Article |
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| ispartof | Journal of computational physics, 2005-12, Vol.210 (2), p.535-553 |
| issn | 0021-9991 1090-2716 |
| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Analytical solutions Atmospheric flow Computational techniques Exact sciences and technology Mathematical methods in physics Physics Shallow water equations |
| title | Unsteady analytical solutions of the spherical shallow water equations |
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