Bifurcations and dynamics in convection with temperature-dependent viscosity in the presence of the O(2) symmetry.
We focus on the study of a convection problem in a two-dimensional 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 are found. We explore the impact of the symmetry on the time evolution of this type of fluid, and we 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 presence of symmetry, 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 in the presence of the O(2) symmetry, thus confirming the determining role of the symmetry in the dynamics.
Instituto de Ciencias Matemáticas (CSIC-UAM-UCM-UC3M), Nicolás Cabrera, 13-15, 28049 Madrid, Spain and Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain.
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J
Curbelo
A M
AM
Mancho