This paper presents a numerical investigation of Soret-driven convection in a horizontal layer of a binary liquid mixture. The layer is confined between rigid, impermeable boundaries and is subject to a prescribed vertical heat flux, which corresponds to the boundary walls of a low thermal conductivity. In the present study, we focus on typical liquid solutions for which instability can occur under both heating from above and heating from below. The linear stability analysis predicts longwave modes over the whole parameter range. However, our direct nonlinear simulations reveal that this longwave behavior is confined to the immediate vicinity of the convection onset. As the Rayleigh number increases, a transition to shorter wavelength convection is observed, a phenomenon particularly pronounced for heating from above. While the linear theory predicts oscillatory convection for heating from below, nonlinear computations show that these oscillations exist near the threshold; however, a more detailed investigation of the oscillatory regimes is needed and will be undertaken in future work. In contrast to the case of perfectly conducting boundaries, convection mainly takes the form of square or rectangular cells. These findings confirm the linear theory near the convection threshold and improve our understanding of complex three-dimensional convective dynamics.
Prokopev et al. (Mon,) studied this question.