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

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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.

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Data Availability Statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors are grateful to two anonymous reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. School of Earth and Environmental Sciences, Seoul National University, Seoul, 08826, South Korea

    Sungju Moon, Jong-Jin Baik & Beom-Soon Han

  2. Max Planck Institute for Meteorology, Bundesstraße 53, 20146, Hamburg, Germany

    Jaemyeong Mango Seo

Authors
  1. Sungju Moon
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  2. Jong-Jin Baik
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  3. Jaemyeong Mango Seo
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  4. Beom-Soon Han
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Corresponding author

Correspondence to Jong-Jin Baik.

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Funding

This work was supported by the Small Grant for Exploratory Research (SGER) program through the National Research Foundation of Korea (NRF-2018R1D1A1A02086007).

Conflict of interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Code availability

The MATLAB and Fortran custom codes used in this study are available from the corresponding author upon request.

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Moon, S., Baik, JJ., Seo, J.M. et al. Effects of density-affecting scalar on the onset of chaos in a simplified model of thermal convection: a nonlinear dynamical perspective. Eur. Phys. J. Plus 136, 92 (2021). https://doi.org/10.1140/epjp/s13360-020-01047-7

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