Stability analysis of stratified Rayleigh-Bénard-Poiseuille convection: Influence of the shear flow

The presence of horizontal flow in stratified systems where a vertical temperature gradient leads to heat transfer through natural convection can be observed in several technological and natural phenomena. In the study reported herein, a linear stability analysis using normal modes and the direct simulation of the governing equations using CFD techniques are applied to investigate the influence of the horizontal flow intensity on the onset of natural convection in a double-layer system heated from below. The results obtained with the two methodologies are in good agreement and complement each other, since, while linear analysis is suitable for defining the critical Rayleigh values, direct simulations allow a detailed analysis of the flow field when the convective motion is fully developed. Due to the large number of phenomena governing the system stability, this study focuses on a part of the spectrum of parameters selected to allow the determination of the minimum values that the Rayleigh number must achieve in order to make natural convection possible. The aim of the study is to gain a better understanding of some basic characteristics of the flow, such as the influence of the boundary conditions and the most common ways in which the convective cells can develop. The results are consistent with previously published data for double-layer Rayleigh-Bénard and single-layer Rayleigh-Bénard-Poiseuille convection. However, the existence of different modes that can make the system unstable creates a more complex scenario for some intervals of the governing parameters.