MHD convection in a horizontal porous-layer filled by a plasma, imbedded in a transverse magnetic field and heated from below, is investigated. The critical Rayleigh number is found and, in simple algebraic closed forms, conditions necessary and sufficient for the onset of steady and oscillatory convection are obtained. It is shown that the stabilizing effect of the magnetic field grows with Q2, Q being the Chandrasekhar number. The linearization principle (Rionero, Rend Lincei Mat Appl 25:368, 2014): “Decay of linear energy for any initial data implies decay of nonlinear energy at any instant” continues to hold also in the case at stake and allows to recover for the global nonlinear stability the conditions of linear stability.
Porous MHD convection: stabilizing effect of magnetic field and bifurcation analysis / Capone, Florinda; Rionero, Salvatore. - In: RICERCHE DI MATEMATICA. - ISSN 1827-3491. - 65:1(2016), pp. 163-186. [10.1007/s11587-016-0258-z]
Porous MHD convection: stabilizing effect of magnetic field and bifurcation analysis
CAPONE, FLORINDA
;RIONERO, SALVATORE
2016
Abstract
MHD convection in a horizontal porous-layer filled by a plasma, imbedded in a transverse magnetic field and heated from below, is investigated. The critical Rayleigh number is found and, in simple algebraic closed forms, conditions necessary and sufficient for the onset of steady and oscillatory convection are obtained. It is shown that the stabilizing effect of the magnetic field grows with Q2, Q being the Chandrasekhar number. The linearization principle (Rionero, Rend Lincei Mat Appl 25:368, 2014): “Decay of linear energy for any initial data implies decay of nonlinear energy at any instant” continues to hold also in the case at stake and allows to recover for the global nonlinear stability the conditions of linear stability.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
