Transition from hexagons to rolls in convection in fluids under non-Boussinesq conditions

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Abstract
The transition between hexagons and rolls in convective patterns has been studied. The transition thresholds and changes in the Nusselt number are discussed theoretically in terms of calculations made by Busse (1967a) and with amplitude equations. Experiments have been done in a shallow layer of pure water under non-Boussinesq conditions using complementary techniques: shadowgraph (qualitative), optical (based on the deflections of a laser beam) and calorimetric. The experimental values of the critical Rayleigh number Rc and the critical wavenumber kc are in agreement with theoretical ones. However, theory and experiments show some discrepancies in the slopes of the non-dimensional convective heat flow curve and in the thresholds of the hysteretic hexagons-rolls transition. These discrepancies are discussed in terms of lateral effects and of the presence of defects in the pattern.

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