Linear and weakly nonlinear multi-diffusive convection in a Navier-Stokes-Voigt fluid layer

The stability of a triply diffusive Voigt fluid layer, where fluid density is influenced by three stratifying agents with different diffusivities (e.g. heat, solute, and another solute like a third agent), has been examined. The linear stability analysis of the problem reveals several unique behaviours not typically observed in single or double diffusive fluid layers. Analytical expressions for the onset of both steady and oscillatory convection are derived from linear stability analysis. The presence of the Voigt fluid increases the threshold value of the Rayleigh numbers, especially the solute Rayleigh number, favouring oscillatory convection. Additionally, disconnected closed oscillatory neutral curves are observed for certain physical parameter selections, representing the need of three critical Rayleigh numbers to define the linear instability criteria, rather than the conventional single value. A weakly nonlinear stability analysis using an improved perturbation technique leads to the derivation of the Ginzburg–Landau equation. The stability of oscillatory bifurcating non-trivial equilibrium solutions and their implications for heat and mass transfer are explored. The oscillatory finite amplitude solution can bifurcate either subcritically or supercritically, depending on the governing parameters. The impact of the Voigt parameter, Rayleigh numbers for each stratifying agent, and diffusivity parameters on oscillatory convection modes for heat and mass transfer is thoroughly analyzed.