A linear magnetic Bénard problem with tensorial electrical conductivity

Georgescu, A. ; Palese, L. ; Redaelli, A.

Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 1, pp. 197-214

Résumé

For normal mode perturbations, in the hypothesis that the principle of exchange of stabilities holds, the eigenvalue problem defining the neutral curves of the linear stability for a magnetic electroanisotropic Benard problem is solved by Budiansky-DiPrima method. The unknown functions are taken as Fourier series on some total sets of separable Hilbert spaces and the expansion functions satisfied only part of the boundary conditions of the problem. This introduces some constraints to be satisfied by the Fourier coefficients. In order to keep the number of these constraintsas low as possible we are lead to use total sets for the even velocity and temperature fields different from the case when velocity and temperature are odd.The splitting ofthe unknown functions into even and odd parts leads to two problems of the sameorder as the given one each of which containing even as well as odd order parts of these functions. The secular equations involve series which are truncated to one and two terms, the last situation corresponding to best results. A closed form of the neutral curve is obtained. The presence of the Hall currents is proved to be destabilizing.