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Remarks on Rotating Shallow-water Magnetohydrodynamics : Volume 20, Issue 5 (29/10/2013)

By Zeitlin, V.

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Book Id: WPLBN0003990805
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File Size: Pages 6
Reproduction Date: 2015

Title: Remarks on Rotating Shallow-water Magnetohydrodynamics : Volume 20, Issue 5 (29/10/2013)  
Author: Zeitlin, V.
Volume: Vol. 20, Issue 5
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2013
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Zeitlin, V. (2013). Remarks on Rotating Shallow-water Magnetohydrodynamics : Volume 20, Issue 5 (29/10/2013). Retrieved from http://www.ebooklibrary.org/


Description
Description: Institut Universitaire de France, Laboratoire de Météorologie Dynamique, UMR8539, CNRS – University P. and M. Curie and Ecole Normale Supérieure, Paris, France. We show how the rotating shallow-water MHD model, which was proposed in the solar tachocline context, may be systematically derived by vertical averaging of the full MHD equations for the rotating magneto fluid under the influence of gravity. The procedure highlights the main approximations and the domain of validity of the model, and allows for multi-layer generalizations and, hence, inclusion of the baroclinic effects. A quasi-geostrophic version of the model, both in barotropic and in baroclinic cases, is derived in the limit of strong rotation. The basic properties of the model(s) are sketched, including the stabilizing role of magnetic fields in the baroclinic version.

Summary
Remarks on rotating shallow-water magnetohydrodynamics

Excerpt
Shecter, D. A., Boyd, J. F., and Gilman, P. A.: Shallow-water magnetohydrodynamic waves in the solar tachocline, Astrophys. J. Lett, 551, L185–L188, 2001.; Ripa, P.: On improving a one-layer ocean model with thermodynamics, J. Fluid Mech., 303, 169–207, 1995.; Bouchut, F.: Ch. 4, in: Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances, edited by: Zeitlin, V., Elsevier, NY, 2007.; Dellar, P. J.: Hamiltonian and symmetric hyperbolic structure of shallow water magnetohydrodynamics, Phys. Plasmas, 9, 1130–1136, 2002.; Dellar, P.: Common Hamiltonian structure of the shallow water equations with horizontal temperature gradients and magnetic fields, Phys. Fluids, 15, 292–297, 2003.; Dikpati, M. and Gilman, P. A.: Prolateness of the solar tachocline inferred from latitudinal force balance in a magnetohydrodynamic shallow water model, Astrophys. J., 552, 348–353, 2001a.; Dikpati, M. and Gilman, P. A.: Flux-transport dynamos with alpha-effect and global instability of tachocline differential rotation: a solution for magnetic parity selection in the sun, Astrophys. J., 559, 428–442, 2001b.; Gilman, P. A.: Magnetohydrodynamic shallow water equations for the solar tachocline, , Astrophys. J. Lett, 544, L79–L82, 2000.; Pedlosky, J.: Geophysical Fluid Dynamics, Springer, NY, 1982.; Rachid, F. Q., Jones, C. A., and Tobias, S. M.: Hydrodynamic instabilities in the solar tachocline, Astronomy Astrophysics, 488, 819–827, 2008.; Reznik, G., Zeitlin, V., and BenJelloul, M.: Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow water model, J. Fluid Mech., 445, 93–120, 2001.; Tobias, S. M., Diamond, P. H., and Hughes, D. W.: Beta-plane magnetohydrodynamic turbulence in the solar tachocline, Astrophys. J. Lett., 667, L113–L116, 2007.; Umurhan, O. M.: The equations of magnetogeostrophy, arXiv:1301.0285v1, 2013.; Zeitlin, V.: On the structure of phase-space, Hamiltonian variables and statistical approach to the description of 2-dimensional hydrodynamics and magnetohydrodynamics, J. Phys A, L171–L175, 1992.; Zeitlin, V. (Ed.): Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances, Elsevier, NY, 2007.; Zeitlin, V., Reznik, G., and BenJelloul, M.: Nonlinear theory of geostrophic adjustment. Part 2. Two-layer and continuously stratified primitive equations, J. Fluid Mech., 491, 207–228, 2003.

 

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