Linear Stability Analysis and Direct Numerical Simulation of Double-Layer Rayleigh-Bénard Convection

Natural convection in superimposed layers of fluids heated from below is commonly observed in many industrial and natural situations, such as crystal growth, co-extrusion processes and atmospheric flow. The stability analysis of this system reveals a complex dynamic behavior, including potential multiplicity of stationary states and occurrence of periodic regimes. In the present study, a linear stability analysis (LSA) is performed to determine the onset of natural convection as a function of imposed boundary conditions, geometrical configuration and specific perturbations. To investigate the effects of the non-linear terms neglected by the LSA, a direct simulation of the full nonlinear problem is performed using computational fluid dynamics (CFD) techniques. The numerical simulations results show an excellent agreement with the LSA results near the convection onset and an increase in the deviation as the Rayleigh number increases above the critical value.