Stability Analysis of Stratified Rayleigh-Bénard-Poiseuille Convection. Part III: Interface Deformation

Interface deformation is a common phenomenon in multi-layered systems that can significantly impact the velocity and temperature fields. In order to track the interface position in a two-layered system subjected to vertical temperature gradient and shear flow, techniques of linear stability analysis (LSA) and computational fluid dynamics (CFD) were applied. The LSA results show that the interface can be deformed for low Reynolds numbers if the fluids in each layer have different viscosity or thermal conductivity or if the thermocapillary effect is significant. The interface can be stabilized by increasing the ratio between the density of each fluid. The limits where the interface deformation can be neglected are defined for several cases. Comparisons with CFD results reveal that the linear analysis is consistent near the convection onset; however, as the Rayleigh number is increased and the non-linear terms become more significant, strong interface deformation can occur and the linear approximation no longer predicts the system behavior.