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

TL;DR

This paper investigates how temperature-dependent viscosity and O(2) symmetry influence convection patterns, revealing new dynamic behaviors like traveling waves and chaos, which are similar to phenomena in other symmetric systems.

Contribution

It introduces the first analysis of convection with temperature-dependent viscosity under O(2) symmetry, highlighting the role of symmetry in complex fluid dynamics.

Findings

Diverse plume morphologies including spout and mushroom shapes.

Discovery of traveling waves, heteroclinic connections, and chaotic regimes.

Symmetry significantly influences the convection dynamics.

Abstract

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.