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

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 alpha < 45 & DEG;, the wavenumber of critical perturbations is equal to zero, and for alpha > 45 & DEG;, 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.

Automated summary

This study focuses on thermal buoyancy convection in an inclined porous layer saturated with fluid. The research shows that three-dimensional perturbations are more dangerous than two-dimensional ones, with the angle of inclination of the layer playing a significant role in the disturbances.