The TRR 181 seminar is held by Dr. Sungju Moon (Nevada State College) on May 25, Bundesstr. 53 20146 Hamburg, room 22/23.

A comparison of generalized Lorenz models to the Boussinesq model and investigations into chaotic properties

Abstract

The Lorenz ’63 system is a three-dimensional system of ordinary differential equations, originally derived as a minimal model for chaotic and intermittent atmospheric motions by considering the lowest order of harmonics in the two-dimensional Rayleigh–Bénard convection problem. Despite its seeming importance in meteorology and beyond, it is not clear whether the much-discussed chaos in the Lorenz system is in fact representative of the dynamics of even the two-dimensional Rayleigh–Bénard convection, let alone that of the atmosphere. In this study, we take a look at a few different generalizations of the Lorenz ’63 system derived by relaxing some of the simplifying assumptions, namely, consideration of higher-order harmonics in the vertical [1], additional physical considerations [2], etc. The exploration of the parameter space leads to some interesting observations involving chaos, intermittency, and their coexistence. Lastly, we derive a fully generalized Lorenz system having an arbitrary number of harmonics in both the vertical and horizontal directions [3]. The numerical solutions of these higher-order generalizations of the Lorenz systems are then compared order-by-order against the solutions of a two-dimensional direct numerical simulation.

References

[1] S. Moon, J. M. Seo, and J.-J. Baik. High-dimensional generalizations of the Lorenz system and implications for predictability. Physica Scripta, 95:085209, 2020.

[2] S. Moon, J. M. Seo, B.-S. Han, and J.-J. Baik. A physically extended Lorenz system. Chaos, 29:063129, 2019.

[3] J. Park, S. Moon, J. M. Seo, and J.-J. Baik. Systematic comparison between the generalized Lorenz equations and DNS in the two-dimensional Rayleigh–Bénard convection. Chaos, 31:073119, 2021.