On baroclinic stability with application to the theory of Kelvin--Helmholtz in MHD

Y. Laghouati¹ - A. Bouabdallah² - A. Alemany³

¹ Department of Physics, Faculty of Sciences, USTO, PB 1505 El Mnaouar, 31000 Oran, Algeria
² Laboratory of Thermodynamics and Energetical Systems, Faculty of Physics, USTHB, PB 32 El Alia, Bab Ezzouar, 16111 Algiers, Algeria
³ Laboratory LEGI, Pamir team-BP 53, 38 041 Grenoble cedex 09, France

Abstract
The researches on the Kelvin--Helmholtz instability have attracted the interest of many authors such as E.T.~Eady and P.H.~Stone. This problem can be represented as a model of the baroclinic instability in atmospheric sciences, for example, a thermal wind in inviscid, stratified, rotating geostrophic systems. Another relevant similar phenomenon can occur in oceanography and astrophysics studied, in particular, by P.G.~Drazin and W.H.~Reid, and also by S.~Chandrasekhar. The Kelvin--Helmholtz instability results from the dynamical interface of two fluid layers with different densities in relative motion. This work is devoted to establishing a criterion of marginal stability when an uniform magnetic field is acting in the streamwise direction. In the light of our analysis, we note that this study may be related to the dynamics of baroclinic instability. Figs 5, Refs 7.