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• W3100623215 abstract "Abstract Kolmogorov flow in two dimensions – the two-dimensional (2D) Navier–Stokes equations with a sinusoidal body force – is considered over extended periodic domains to reveal localised spatiotemporal complexity. The flow response mimics the forcing at small forcing amplitudes but beyond a critical value develops a long wavelength instability. The ensuing state is described by a Cahn–Hilliard-type equation and as a result coarsening dynamics is observed for random initial data. After further bifurcations, this regime gives way to multiple attractors, some of which possess spatially localised time dependence. Co-existence of such attractors in a large domain gives rise to interesting collisional dynamics which is captured by a system of 5 (1-space and 1-time) partial differential equations (PDEs) based on a long wavelength limit. The coarsening regime reinstates itself at yet higher forcing amplitudes in the sense that only longest-wavelength solutions remain attractors. Eventually, there is one global longest-wavelength attractor which possesses two localised chaotic regions – a kink and antikink – which connect two steady one-dimensional (1D) flow regions of essentially half the domain width each. The wealth of spatiotemporal complexity uncovered presents a bountiful arena in which to study the existence of simple invariant localised solutions which presumably underpin all of the observed behaviour." @default.
• W3100623215 created "2020-11-23" @default.
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• W3100623215 date "2014-06-10" @default.
• W3100623215 modified "2023-10-01" @default.
• W3100623215 title "Spatiotemporal dynamics in two-dimensional Kolmogorov flow over large domains" @default.
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• W3100623215 doi "https://doi.org/10.1017/jfm.2014.270" @default.
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