Articles | Volume 20, issue 5
Nonlin. Processes Geophys., 20, 893–898, 2013
Nonlin. Processes Geophys., 20, 893–898, 2013

Research article 29 Oct 2013

Research article | 29 Oct 2013

Remarks on rotating shallow-water magnetohydrodynamics

V. Zeitlin V. Zeitlin
  • Institut Universitaire de France, Laboratoire de Météorologie Dynamique, UMR8539, CNRS – University P. and M. Curie and Ecole Normale Supérieure, Paris, France

Abstract. 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.