Geostrophic vs magneto-geostrophic adjustment and nonlinear magneto-inertia-gravity waves in rotating shallow water magnetohydrodynamics

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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Contributor : François Bouchut <>
Submitted on : Sunday, September 27, 2015 - 5:35:41 PM
Last modification on : Thursday, July 18, 2019 - 3:00:04 PM

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Vladimir Zeitlin, Christelle Lusso, François Bouchut. Geostrophic vs magneto-geostrophic adjustment and nonlinear magneto-inertia-gravity waves in rotating shallow water magnetohydrodynamics. Geophysical and Astrophysical Fluid Dynamics, Taylor & Francis, 2015, 109 (5), pp.497-523. ⟨10.1080/03091929.2015.1072178⟩. ⟨hal-01205761⟩

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