# Laboratoire de Mécanique des Fluides et d’Acoustique - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

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Article dans Phys. Rev. E (2015)

## Transition from multiplicity to singularity of steady natural convection in a tilted cubical enclosure

Juan F. Torres, Daniel Henry, Atsuki Komiya & Shigenao Maruyama

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 ($\theta\approx0\text{°}$), 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 $\theta\approx0\text{°}$ disappear, eventually resulting in the single steady roll solution found in the heated-from-the-sides configuration ($\theta=90\text{°}$). We confirm the existence of critical angles during the transition $\theta:\;0\text{°}\rightarrow90\text{°}$, and we demonstrate that such angles are a consequence of either singularities or collisions of bifurcation points in the Rayleigh-number-$\theta$ parameter space. We finally derive the most important critical angles corresponding to any Newtonian fluid of Prandtl number greater than that of air.