Reduction of SO(2) symmetry for spatially extended dynamical systems

Physical Review Letters
Nazmi Burak BudanurEvangelos Siminos

Abstract

Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of equivalent solutions obtained from it by a translation or a rotation. This multitude of equivalent solutions tends to obscure the dynamics of turbulence. Here we describe the "first Fourier mode slice," a very simple, easy to implement reduction of SO(2) symmetry. While the method exhibits rapid variations in phase velocity whenever the magnitude of the first Fourier mode is nearly vanishing, these near singularities can be regularized by a time-scaling transformation. We show that after application of the method, hitherto unseen global structures, for example, Kuramoto-Sivashinsky relative periodic orbits and unstable manifolds of traveling waves, are uncovered.

References

Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yueheng Lan, Predrag Cvitanović
Jan 3, 2013·Chaos·Predrag CvitanovićEvangelos Siminos
Jun 19, 2013·Physical Review Letters·M AvilaB Hof

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Citations

Aug 4, 2015·Chaos·Nazmi Burak BudanurPredrag Cvitanović
Jul 26, 2016·Physical Review Letters·X DingK A Takeuchi
Mar 18, 2016·Physical Review. E·Ashley P WillisPredrag Cvitanović
Feb 3, 2019·Chaos·Nazmi Burak Budanur, Marc Fleury
Jul 22, 2020·Physical Review. E·Alec J Linot, Michael D Graham
Dec 18, 2020·Physical Review. E·D Lasagna
Jul 3, 2021·Physical Review Letters·Gökhan YalnızNazmi Burak Budanur

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