Linear and nonlinear analyses of double-diffusive convection in couple-stress fluids within a Brinkman porous framework under variable gravity

This study examines the linear and nonlinear stability of thermosolutal convection in a couple-stress fluid layer saturating a Brinkman-type porous medium under variable gravity. Three representative gravity profiles are considered to model non-uniform terrestrial and microgravity environments. Linear (normal-mode) and nonlinear (energy) analyses are employed to determine the critical Rayleigh number for different boundary combinations. Results reveal that both the Brinkman number and the couple-stress parameter raise the critical Rayleigh number, enhancing system stability, while the solute Rayleigh number promotes instability. Gravity variation exerts a dual influence: decreasing gravity with height stabilizes the system, whereas increasing gravity enhances convection, with a quadratic decrease yielding nearly twice the stabilization of the linear case. The close agreement between linear and nonlinear thresholds confirms global stability and eliminates subcritical bifurcation. The study underscores the interplay of microstructural stresses, porous resistance, and gravity variation in controlling convective behaviour across complex fluid environments.