## Abstract

We consider the onset of convective instability in an inclined porous layer heated from below. Linearised stability theory tells us that there always exists a band of wavenumbers within which small-amplitude disturbances will grow, but this is true only when the inclination of the layer is less than 31.49032
^{∘}. At higher inclinations such disturbances always decay. However, it is also widely known that nonlinear convection may be computed for larger inclinations. This paper provides an initial explanation for how these two facts may be reconciled. It is generally assumed that the onset of convection in an inclined layer is supercritical, and, while this is certainly true when the layer is horizontal, there is no reason to assume that it remains so for other inclinations. The present paper, then, is a combined weakly-nonlinear and numerical investigation of the effect of inclination on the manner of onset. The weakly nonlinear analysis shows that the transition from a supercritical onset to a subcritical one takes place when the inclination is 24.247627
^{∘}, and this is confirmed using a detailed and focussed set of nonlinear numerical simulations.

Original language | English |
---|---|

Article number | 103992 |

Journal | Mechanics Research Communications |

Volume | 125 |

Early online date | 28 Sept 2022 |

DOIs | |

Publication status | Published - 31 Oct 2022 |

## Keywords

- Finite difference methods
- Free convection
- Porous media
- Subcritical instability
- Weakly nonlinear theory

## ASJC Scopus subject areas

- Civil and Structural Engineering
- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering