## Convective stability of CO$$_2$$ sequestration in a porous medium.(English)Zbl 07446961

Summary: We considered an incompressible fluid-saturated porous layer bounded by two infinite parallel plates. The Boussinesq approximation and Darcy’s law are applied. The permeability is assumed to be a linear function of the depth $$z$$. The linear stability is investigated. The long wavelength expansion method is applied to conduct the weakly nonlinear stability analysis. The evolution equation is derived and analyzed. A uniformly valid periodic solution of the evolution equation is obtained by the application of the Poincaré-Lindstedt method. Some numerical simulations are presented.

### MSC:

 76E20 Stability and instability of geophysical and astrophysical flows 76E15 Absolute and convective instability and stability in hydrodynamic stability 76S05 Flows in porous media; filtration; seepage 76-10 Mathematical modeling or simulation for problems pertaining to fluid mechanics 76E06 Convection in hydrodynamic stability
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### References:

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