Two-dimensional thermal convection in porous enclosure subjected to the horizontal seepage and gravity modulation

Abstract

Coupled effect of horizontal seepage and gravity modulation on the onset and nonlinear regimes of two-dimensional thermal buoyancy convection in horizontal fluid-saturated porous cylinder of rectangular cross section with perfectly conductive boundaries is studied. It is shown that gravity modulation makes destabilizing effect. Null-dimensional dynamical system describing supercritical convective regimes is derived. Conditions for existence of stable periodical regimes are defined. It is found that system demonstrates dynamics on a torus which can be either resonant or non-resonant depending on the parameters. Synchronization domains which correspond to the resonant torus existence in the parameter space are determined by the rotation number technique. It is found that at certain values of the ratio of the cross section height to width, degeneracy takes place. In this case different stable periodical regimes forming one-parametric family coexist. Linear stability and nonlinear dynamics of the system at finite values of the parameters are studied numerically by finite difference method.