K. Fujimura and M. Nagata: Degenerate 1:2 steady mode interaction - MHD flow in a vertical slot, Physica D115 (1998) 377-400.

Abstract

Degenerate bifurcations resulting from 1:2 mode interaction between quasi-neutral steady modes in MHD natural convection have been investigated on a weakly nonlinear basis. In the limit of small Prandtl number and small magnetic Prandtl number, two types of nonlinearly degenerate situations are found to take place for relatively low Hartmann numbers, 4.0432 and 8.7701. The amplitude equations of the quintic order are derived by means of the center manifold reduction. The entire picture of the bifurcation is obtained for the actual numerical values of the coefficients in the amplitude equations. A fully nonlinear numerical analysis of the hydrodynamic equations is also carried out. The local characteristics predicted by the amplitude equations are found to be justified.