Onset and nonlinear regimes of convection in an inclined porous layer subject to a vertical temperature gradient

Abstract

In this paper, we study the onset and non-linear regimes of thermal buoyancy convection in an inclined porous layer saturated with fluid. The layer is subject to a gravitational field and a strictly vertical temperature gradient. This problem is important for geological applications. The linear stability of the heat-conducting regime to two-dimensional perturbations was previously studied by Kolesnikov and Lyubimov [J. Appl. Mech. Tech. Phys. 14, 400–404 (1973)]. In the first part of our work, we numerically, using the finite difference method, investigate two-dimensional nonlinear convection regimes that arise after the loss of stability of the heat-conducting regime. In the second part of the paper, the linear stability of the heat-conducting regime to three-dimensional perturbations is investigated. It has been found that for any layer inclination angle, three-dimensional perturbations are more dangerous than two-dimensional ones, and the most dangerous perturbations have the form of longitudinal rolls. For the layer inclination angle α<45°, the wavenumber of critical perturbations is equal to zero, and for α>45°, it differs from zero. Numerical calculations by the finite volume method within the framework of the full three-dimensional nonlinear approach confirm the conclusions of the linear stability analysis.