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Updated: Feb 8, 2026

Thermocapillary Convection Space Experiment on the SJ-10 Recoverable Satellite
Published on: March 11, 2020
Three-dimensional instabilities of natural convection between two differentially heated vertical plates: Linear and
Zhenlan Gao1,2,3, Berengere Podvin1, Anne Sergent1,2
1LIMSI, CNRS, Université Pari-Saclay, Campus Universitaire, run Von Neumann, 91400 Orsay, France.
Abstract:
The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Ra_{c}, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration. In all cases the 2D rolls are destabilized in the spanwise direction. Efficient linear stability analysis based on an Arnoldi method shows competition between two eigenmodes, corresponding to different spanwise wavelengths and different types of roll distortion. Nonlinear integration shows that the lower-wave-number mode is always dominant. A partial route to chaos is established through the nonlinear simulations. The flow becomes temporally chaotic for Ra=1.05Ra_{c}, but remains characterized by the spatial patterns identified by linear stability analysis. This highlights the complementary role of linear stability analysis and nonlinear simulation.
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