Effects of density-affecting scalar on the onset of chaos in a simplified model of thermal convection: a nonlinear dynamical perspective

Abstract

To explore how density-affecting scalar influences the onset of chaos in a simplified model of thermal convection, we consider three versions of a physically extended Lorenz system obtained from incorporating additional physical ingredients such as rotation and density-affecting scalar. The three versions of the extended Lorenz system correspond to the cases when the density-affecting scalar has positive, neutral, and negative impacts on buoyancy. In general, compared to the case when the density-affecting scalar has a positive (neutral) impact on buoyancy, the case when the density-affecting scalar has a neutral (negative) impact on buoyancy leads to a higher critical Rayleigh parameter, a sign of delayed onset of chaos. For an appropriate choice of parameters that lead to chaotic solutions in all three cases, it is shown that the chaotic attractors for the three cases can exhibit a variety of different characteristics, such as taking on the shape of the classic Lorenz attractor, sharing the phase space with stable point attractors, and taking an unusual shape that is distinguished from the Lorenz attractor. The different characteristics in chaotic attractors lead to qualitative differences in the behaviour exhibited by the corresponding flow and temperature patterns reconstructed from the numerical solutions. Further analysis of this simplified model offering a nonlinear dynamical perspective on the thermal convection problem is expected to serve as an avenue for gaining new insights into this and related problems.