Thermosolutal Convection in a Brinkman–Darcy–Kelvin–Voigt Fluid of Order One with Couple Stresses Effect

We introduce a framework for analysing thermosolutal convection within a Kelvin–Voigt fluid of first order using a Brinkman–Darcy porous medium. This setup involves heating and salting from below, leading to a scenario where the thermal and solutal gradients compete: Thermal gradients tend to destabilise the system, whereas solutal gradients have a stabilising effect. Additionally, we explore scenarios where heating occurs from below while salting is introduced from above. This study examines how couple stresses affect the dynamics. We calculate the threshold at which instability occurs, noting the complexity of the instability surface’s shape. Factors such as the Kelvin–Voigt property, couple stresses, Brinkman, and Prandtl numbers are significant, stabilising forces, especially when the convection exhibits oscillatory behaviour. Details on the instability surface’s quantitative aspects are provided. Furthermore, we touch upon the issue of nonlinear stability in this context.