Filtration convection in an annular domain and branching of a family of steady-state regimes

Abstract

A plane problem of convection of incompressible fluid saturating a porous annular domain is considered. Using the Darcy model and a finite-differencemethod, which retains the cosymmetry of the original problem, we investigate the branching of a family of steady-state regimes from the mechanical equilibrium. The evolution of convective motions with increase in the Rayleigh number is studied and the onset of instability on the family of steady-state regimes is analyzed. For narrow annular domains, the cosymmetric effect of a delay in the branching of a secondary self-oscillation mode from the family is detected, while for domains of moderate thickness and sectors the monotonic instability is typical.