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Convection and instabilities in the Rayleigh-Bénard situation (Soret, Marangoni effects, inclination)

Convection and instabilities in the Rayleigh-Bénard situation (Soret, Marangoni effects, inclination)

Daniel Henry, Hamda Ben Hadid, F. Torres, A. Komiya, S. Maruyama, A. Bergeon, E. Knobloch

These studies were motivated by spatial experiments either for Soret effect measurements realized by the département de Physique des matériaux de l’université Lyon 1, or for the characterization of the Marangoni convection realized by the Microgravity Research Center of the Université libre de Bruxelles, and by a collaboration with the University of Tohoku (Japan).

Our more recent studies using continuation method were performed within the frame of Felipe Torres PhD and concerned the convection in heated cavities submitted to an inclination. We considered a slightly elongated cavity with a square cross-section and a cubical cavity. The results show the influence of the inclination which, due to the broken symmetries, change the bifurcations between the different solution branches. They also show the coexistence of numerous different solutions for given parameter values, particularly in the case of the cubical cavity and for small inclinations [A109, A110, A116].

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Bifurcation diagram for a cubical cavity inclined by 0.1 degree: we can see the effect of a slight inclination on the solution branches originated at the same bifurcation point in the horizontal case. The figures give the vertical velocity at mid-height in the cavity: solid lines for positive isovalues, dashed lines for negative isovalues.

Older work: Soret effect, Marangoni effect, porous media.

The studies first concern flows initiated by buoyancy forces in vertical cylinders [A2, A15, A18] or inclined cylinders [A7, A10, A11] in configurations corresponding to ground-based or microgravity Soret effect measurements [A3, A5, A6, A9, A35].

We then considered Marangoni-Bénard situations (surface tension forces) in 2D or 3D cavities for binary mixtures with Soret effect [A24, A26, A28, A38, A41, A51, A64]. The objectives of the work were the determination and characterization of the different hydrodynamic regimes as a function of the problem parameters. The first studies were performed by direct numerical simulation whereas, later, continuation methods were used. These methods allow to follow the steady solution branches (stables or unstables) and to localize the bifurcation points, giving well documented bifurcation diagrams. Another study then concerned the 3D cavity with square or nearly square cross-section where the bifurcation diagrams have been shown to strongly depend on the symmetry properties [A56] (collaboration with A. Bergeon and E. Knobloch). We also used the continuation method to study the convection in porous medium in a square cavity [A103].

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Convective solutions co-existing at Ra=300 in a square porous cavity.