### Abstract

The transition from the complex Rayleigh-Bénard convection to the simple heated-from-the-sides configuration in a cubical cavity filled with a Newtonian fluid is numerically studied. The cavity is tilted by an angle θ around its lower horizontal edge and is heated and cooled from two opposite tilted sides. We first analyze the effect of a marginal inclination angle on quasi-Rayleigh-Bénard convection (θ≈0), which is a realistic physical approximation to the ideal Rayleigh-Bénard convection. We then yield the critical angles where multiple solutions that were initially found for θ≈0 disappear, eventually resulting in the single steady roll solution found in the heated-from-the-sides configuration (θ=90). We confirm the existence of critical angles during the transition θ:0→90, and we demonstrate that such angles are a consequence of either singularities or collisions of bifurcation points in the Rayleigh-number-θ parameter space. We finally derive the most important critical angles corresponding to any Newtonian fluid of Prandtl number greater than that of air.

Original language | English |
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Article number | 023031 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 92 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 Aug 28 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*92*(2), [023031]. https://doi.org/10.1103/PhysRevE.92.023031