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The Lorenz system began as a truncated model of thermal convection. With colleagues I extended it with rotation, density-affecting scalars and more Fourier modes, to ask how these ingredients change the onset of chaos and what they imply for predictability.
Figure. Trajectories of a physically extended Lorenz system in different parameter regimes (Moon et al. 2019, Chaos).
From Lorenz models to convection
From Lorenz models to convection
Adding a density-affecting scalar delays or advances the onset of chaos depending on whether it lowers or raises buoyancy, and can produce attractors unlike the classic butterfly. High-order generalizations show how the route to chaos and predictability change as more modes are retained, and systematic comparisons with direct numerical simulation (DNS) of two-dimensional Rayleigh–Bénard convection test how far these models reach.
Figure. DNS solution of the streamfunction ψ(x, z) (top) and temperature perturbation θ(x, z) (bottom) at the steady-state equilibrium: a pair of counter-rotating vortices and mushroom-shaped convection (Park et al. 2021, Chaos).
Related papers
Related papers
Park, J., S. Moon, J. M. Seo, and J.-J. Baik (2021). Systematic comparison between the generalized Lorenz equations and DNS in the two-dimensional Rayleigh-Bénard convection. Chaos, 31, 073119.
Moon, S., J.-J. Baik, and J. M. Seo (2021). Chaos synchronization in generalized Lorenz systems and an application to image encryption. Communications in Nonlinear Science and Numerical Simulation, 96, 105708.
Moon, S., J.-J. Baik, J. M. Seo, and B.-S. Han (2021). Effects of density-affecting scalar on the onset of chaos in a simplified model of thermal convection: A nonlinear dynamical perspective. European Physical Journal Plus, 136, 92. doi:10.1140/epjp/s13360-020-01047-7
Moon, S., J. M. Seo, and J.-J. Baik (2020). High-dimensional generalizations of the Lorenz system and implications for predictability. Physica Scripta, 95, 085209. doi:10.1088/1402-4896/ab9d3e
Moon, S., J. M. Seo, B.-S. Han, J. Park, and J.-J. Baik (2019). A physically extended Lorenz system. Chaos, 29, 063129. doi:10.1063/1.5095466
Park, J., P. Billant, J.-J. Baik, and J. M. Seo (2018). Competition between the centrifugal and strato-rotational instabilities in the stratified Taylor-Couette flow. Journal of Fluid Mechanics, 840, 5–24. doi:10.1017/jfm.2018.15
Moon, S., B.-S. Han, J. Park, J. M. Seo, and J.-J. Baik (2017). Periodicity and chaos of high-order Lorenz systems. International Journal of Bifurcation and Chaos, 27, 1750176. doi:10.1142/S0218127417501760
Related presentations
Related presentations
Talk · High-dimensional generalizations of the Lorenz system and implications for predictability · KMS 2020 (Moon et al.)
Talk · Chaos and periodicity of high-order Lorenz systems · KMS 2017 (Moon et al.)
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