H. Herrero et al., DERIVATION OF THE AMPLITUDE EQUATION FOR A HYDROMAGNETIC CONVECTIVE PROBLEM, Zeitschrift fur Physik. B, Condensed matter, 99(3), 1996, pp. 457-463
The amplitude equation for a convective system under a vertical magnet
ic field is derived. The coefficients in these equations have been num
erically calculated for infinite Prandtl number fluids and for boundar
y conditions both free and rigid top and bottom. The results confirm t
hat, for realistic parameter values only stationary convection can be
present and the pattern is made by convective rolls.