Bifurcations from steady to quasi-periodic flows in a laterally heated cavity filled with low Prandtl number fluids

A. Medelfef (1, 2) , D. Henry (1) , A. Bouabdallah (2) , S. Kaddeche (3)

1 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique
2 USTHB - Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]
3 INSAT - Institut National des Sciences Appliquées et de Technologie [Tunis]

This study deals with the transition toward quasi-periodicity of buoyant convection generated by a horizontal temperature gradient in a three-dimensional parallelepipedic cavity with dimensions 4 × 2 × 1 (length × width × height). Numerical continuation techniques, coupled with an Arnoldi method, are used to locate the steady and Hopf bifurcation points as well as the different steady and periodic flow branches emerging from them for Prandtl numbers ranging from 0 to 0.025 (liquid metals). Our results highlight the existence of two steady states along with many periodic cycles, all with different symmetries. The bifurcation scenarios consist of complex paths between these different solutions, giving a succession of stable flow states as the Grashof number is increased, from steady to periodic and quasi-periodic. The change of these scenarios with the Prandtl number, in connection with the crossing of bifurcation points, was carefully analysed.

Mots clés: Bifurcation; buoyant convection; low-Prandtl number

Domaines: Sciences de l'ingénieur [physics]

A. Medelfef, D. Henry, A. Bouabdallah, S. Kaddeche. Bifurcations from steady to quasi-periodic flows in a laterally heated cavity filled with low Prandtl number fluids. Journal of Fluid Mechanics, 2019, 861, pp.223-252. ⟨10.1017/jfm.2018.912⟩. ⟨hal-02356287⟩