Finite-amplitude ferro-convection and electro-convection in a rotating fluid

Abstract

The onset of Rayleigh–Bénard convection in a horizontal ferrofluid layer subjected to rotation with respect to the vertical axis is theoretically investigated in the paper. Using a truncated Fourier series representation, an analytically intractable fifth-order Lorenz model that has two quadratic nonlinearities is derived and then reduced to the analytically tractable Landau equation with cubic nonlinearity using the method of multi-scales. The critical Rayleigh number of the linear stability theory and that of the energy stability method is drawn from other works and compared with that obtained by the weakly nonlinear stability method reported in the paper. It is found that the critical Rayleigh number obtained by the two nonlinear theories predicts subcritical motions. Further, the results on electro-convection in a rotating fluid layer are extracted from the corresponding problem of ferro-convection by establishing an one-to-one correspondence between the governing equations of the two problems.