Chaos in the thermal convection of a Newtonian fluid with a temperature dependent viscosity

The onset of chaotic motion in Newtonian fluid with a temperature dependent viscosity is explored in the context of the Rayleigh-Bénard thermal convection setup. Galerkin truncation is used to derive a low-order dynamical system (generalized Lorenz system) from the governing equations which reduces to the classical Lorenz system for a Newtonian fluid with a constant viscosity. The effect of the temperature dependent viscosity on the nonlinear solutions is analyzed by considering projections in the phase-space. Also, time signature of the solutions is investigated. The onset of chaotic motion is also discussed in detail for different values of temperature dependent viscosity in this paper.