An in-depth numerical study of the two-dimensional Kuramoto-Sivashinsky equation

Proceedings. Mathematical, Physical, and Engineering Sciences
A KalogirouD T Papageorgiou

Abstract

The Kuramoto-Sivashinsky equation in one spatial dimension (1D KSE) is one of the most well-known and well-studied partial differential equations. It exhibits spatio-temporal chaos that emerges through various bifurcations as the domain length increases. There have been several notable analytical studies aimed at understanding how this property extends to the case of two spatial dimensions. In this study, we perform an extensive numerical study of the Kuramoto-Sivashinsky equation (2D KSE) to complement this analytical work. We explore in detail the statistics of chaotic solutions and classify the solutions that arise for domain sizes where the trivial solution is unstable and the long-time dynamics are completely two-dimensional. While we find that many of the features of the 1D KSE, including how the energy scales with system size, carry over to the 2D case, we also note several differences including the various paths to chaos that are not through period doubling.

References

Nov 1, 1989·Physical Review A: General Physics·S TohT Kawahara
Jul 5, 1993·Physical Review Letters·C JayaprakashR Pandit
Jun 5, 1995·Physical Review Letters·R Cuerno, A L Barabási
Nov 20, 1995·Physical Review Letters·M Rost, J Krug
Dec 15, 1991·Proceedings of the National Academy of Sciences of the United States of America·Y S Smyrlis, D T Papageorgiou
Jun 5, 2003·Chaos·Ralf W. Wittenberg, Philip Holmes
May 24, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hector Gomez, José París

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Citations

Apr 18, 2018·Proceedings. Mathematical, Physical, and Engineering Sciences·R J TomlinD T Papageorgiou

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