Electrical anisotropic effects on thermal instability

Steady Convection in MHD Bénard Problem with Hall and Ion-Slip Effects

“…Moreover this semplification must be done in such a way that the energy relation assumes the simplest form. Following this approach in this paper the problem governing the perturbation evolution is reformulated in terms of some essential variables, by splitting the perturbation equations in the solenoidal and potential parts, obtaining some of the equations derived in [33] to study linear instability by the normal modes technique. Differentiating with respect to the parameters involved in the Lyapunov function, we obtained a nonlinear stability bound that coincides with the linear one, in the subspace of the parameter space where instability occurs as stationary convection.…”

“…The right hand side of (91) represents exactly the critical function of linear instability in presence of Hall and ion-slip currents, if the principle of exchange of stabilities holds [33].…”

“…with R * a given by (91), is a sufficient condition of linear and non linear Lyapunov stability, that is, the linear and non linear stability bounds coincide if instability occurs as stationary convection. , (95) where R * is exactly the Rayleigh function of the linear instability theory, if the principle of exchange of stabilities holds [33].…”