Double-diffusive Hadley–Prats flow in a porous medium subject to gravitational variation

• Thermosolutal double-diffusive Hadley porous convection is explored in the presence of mass flow and gravity field variation.
• The destabilising effect of mass flow is demonstrated in both the linear and nonlinear stability analyses.
• Under certain parameter ranges potential subcritical instabilities are present.

A model for double-diffusive porous Hadley–Prats flow under the effect of a variable gravity field is explored. Both linear instability and nonlinear stability analyses are performed to assess the suitability of linear theory to predict the destabilisation of the flow. The resultant eigenvalue problems for both theories are solved using shooting and fourth order Runga–Kutta methods for various flow governing parameters. The results indicate that both the linear and nonlinear results undergo quantitative changes subject to horizontal thermal and solutal gradients along with the presence and absence of gravity and mass flow variations. For certain parameter ranges there are also substantial regions of potential subcritical instability, such that instabilities may arise before the linear stability threshold is reached.