We focus the study of a convection problem in a 2D setup in the presence of
the O(2) symmetry. The viscosity in the fluid depends on the temperature as it
changes its value abruptly in an interval around a temperature of transition.
The influence of the viscosity law on the morphology of the plumes is examined
for several parameter settings, and a variety of shapes ranging from spout to
mushroom shaped is found. We explore the impact of the symmetry on the time
evolution of this type of fluid, and find solutions which are greatly
influenced by its presence: at a large aspect ratio and high Rayleigh numbers,
traveling waves, heteroclinic connections and chaotic regimes are found. These
solutions, which are due to the symmetry presence, have not been previously
described in the context of temperature dependent viscosities. However,
similarities are found with solutions described in other contexts such as flame
propagation problems or convection problems with constant viscosity also under
the presence of the O(2) symmetry, thus confirming the determining role of the
symmetry in the dynamics.Comment: 21 pages, 10 figure
