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We focus the study of a convection problem in a 2D setup in the presence ofthe O(2) symmetry. The viscosity in the fluid depends on the temperature as itchanges its value abruptly in an interval around a temperature of transition.The influence of the viscosity law on the morphology of the plumes is examinedfor several parameter settings, and a variety of shapes ranging from spout tomushroom shaped is found. We explore the impact of the symmetry on the timeevolution of this type of fluid, and find solutions which are greatlyinfluenced by its presence: at a large aspect ratio and high Rayleigh numbers,traveling waves, heteroclinic connections and chaotic regimes are found. Thesesolutions, which are due to the symmetry presence, have not been previouslydescribed in the context of temperature dependent viscosities. However,similarities are found with solutions described in other contexts such as flamepropagation problems or convection problems with constant viscosity also underthe presence of the O(2) symmetry, thus confirming the determining role of thesymmetry in the dynamics.

Bifurcations and dynamics in convection with temperature-dependent viscosity in the presence of the O(2) symmetry