Global nonlinear stability of bidispersive porous convection with throughflow and depth-dependent viscosity

Abstract

The linear instability and the nonlinear stability analyses have been performed to examine the combined impact of a uniform vertical throughflow and a depth-dependent viscosity on bidispersive porous convection using the Darcy theory with a single temperature field. The validity of the principle of exchange of stability is proved. The eigenvalue problems resulting from both linear instability and nonlinear stability analyses with variable coefficients are numerically solved using the Chebyshev pseudo-spectral method. The equivalence of linear instability and nonlinear stability boundaries is established in the absence of throughflow, while in its presence, the subcritical instability is shown to be evident. The stability of the system is independent of the direction of throughflow in the case of constant viscosity, whereas upflow is found to be more stabilizing than downflow when the viscosity is varying with depth. While the viscosity parameter offers a destabilizing influence on the onset of convection in the absence of throughflow, it imparts both stabilizing and destabilizing effects on the same in its presence. The influence of the ratio of permeabilities and the interphase momentum transfer parameter is to make the system more stable. The findings of a mono-disperse porous medium are presented as a specific case within the broader context of this investigation.