A Dynamical System Approach for Finding Nonlinear Flow Structures in Double-gyre Circulation

This work is dedicated to analysing the simulations of the quasi-geostrophic double-gyre model from dynamical systems point of view to discover nonlinear low-order structures in this turbulent regime. The double-gyre is simulated by a stratified quasi-geostrophic model which is solved using high-resolution CABARET scheme [1]. The statistically stationary simulations of the double-gyre model are considered for 400 years after a 100-year spin-up period. Double-gyre simulations are coarse-grained (symbolized) based on the Taken’s embedding theorem [2] which is proved promising for identifying nonlinear patterns from the stochastic background in the turbulent flow signals. To analyse the coarse-grained time series, Permutation Entropy [3-6] is deployed to quantify repetitive mutual ordering between subsequent time series values using the deviations from uniformity in the distribution of occurrences for symbolic ordinal patterns. Based on permutation entropy analysis, the large-scale double-gyre circulation and its eastward jet demonstrate highly nonlinear behaviour while smaller-scale eddies spread throughout the domain behave linearly.  The results of this dynamical system analysis are also compared with data-driven and multi-scale reduced-order models previously developed for this ocean circulation [7,8].

References:

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[5] Kobayashi, W., Gotoda, H., Kandani, S., Ohmichi, Y., & Matsuyama, S. (2019). Spatiotemporal dynamics of turbulent coaxial jet analyzed by symbolic information-theory quantifiers and complex-network approach, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (12), 123110.

[6] Gryazev, V., Riabov, V., Markesteijn, A., Armani, U., Toropov, V., & Karabasov, S. A. (2024). A Dynamical System Method for Finding Flow Structures from Jet LES Data. In 30th AIAA/CEAS Aeroacoustics Conference (2024), 3087.

[7] Naghibi, E., Armani, U., Gryazev, V., Toropov, V., & Karabasov, S., (2024). Reconstruction of the North Atlantic Double-gyre Circulation with Genetic Programming, Springer Proceedings in Mathematics and Statistics, Proceeding of ATSF Conference 2024.

[8] Naghibi, S. E., Karabasov, S. A., Jalali, M. A., & Sadati, S. H. (2019). Fast spectral solutions of the double-gyre problem in a turbulent flow regime. Applied Mathematical Modelling, 66, 745-767.