Longtime persistence of linear dynamic in magnetoconvection

We extend the Chandrasekhar's marginal stability of an infinite conducting fluid layer heated from below and subjected to a vertical magnetic field to non-zero growth rate. We show that this regime is relevant by comparing the linear stability results with direct numerical simulations (DNS). The growth-rate and wavelengths are accurately predicted by the linear eigenvalue problem, even at largely overcritical Rayleigh numbers. Moreover, it is found that the linear dynamics break down when the amplitude of the velocity perturbations is of the order of the characteristic buoyancy velocity $W_{buoy}=\sqrt{g\beta \Delta T h}$, with $g$ the gravitational acceleration, $\beta$ the thermal expansion coefficient, $\Delta T>0$ the bottom-top temperature difference and $h$ the height of the layer. At large timescales, there is no memory phenomenon from the onset of convection: the height of the enclosure is only responsible for the size of the structures.