Geostrophic vs magneto-geostrophic adjustment and nonlinear magneto-inertia-gravity waves in rotating shallow water magnetohydrodynamics |
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Authors: | Vladimir Zeitlin Christelle Lusso François Bouchut |
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Institution: | 1. Laboratory of Dynamical Meteorology, UMR8539, University P. and M. Curie, 75005 Paris, France.;2. Institut Universitaire de France, .;3. Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), CNRS, UPEM, UPEC, Université Paris-Est, F-77454 Marne-la-Vallée, France. |
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Abstract: | The evolution of localised jets and periodic nonlinear waves in rotating shallow water magnetohydrodynamics (rotating SWMHD) and standard rotating shallow water model (RSW) is compared within the framework of translationally-invariant 1.5-dimensional configurations, which are traditionally used in geophysical fluid dynamics for studying geostrophic adjustment and frontogenesis. Such configurations also allow for exact nonlinear wave solutions in both models. A theory of the magneto-geostrophic adjustment, i.e. adjustment of an arbitrary initial configuration to a state of magneto-geostrophic equilibrium in RSWMHD, is developed and confirmed by numerical simulations with a finite-volume well-balanced code. The code is resolving all kinds of waves in the model and corresponding weak solutions equally well. It is benchmarked by reproducing exact solutions – steady essentially nonlinear Alfvèn and mixed magneto-inertia-gravity waves – and used to demonstrate robustness of these solutions with respect to localised along-wave perturbations. It is also shown how the results on adjustment can be extended to the fully 2-dimensional case. |
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Keywords: | Shallow-water magnetohydrodynamics Magneto-geostrophic adjustment Nonlinear Alfvén waves |
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