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arXiv · 1906.06277

The origin of localized snakes-and-ladders solutions of plane Couette flow

Matthew Salewski·John F. Gibson·Tobias M. Schneider
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Abstract

Spatially localized exact solutions of plane Couette flow are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations. [PRL 104,104501 (2010)]. We demonstrate the mechanism by which these snaking solutions originate from well-known periodic states of the Taylor-Couette system. They are formed by a localized slug of Wavy-Vortex flow that emerges from a background of Taylor vortices via a modulational sideband instability. This mechanism suggests a deep connection between pattern-formation theory and Navier-Stokes flow.

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Matthew Salewski, John F. Gibson, Tobias M. Schneider. 2019-06-14. The origin of localized snakes-and-ladders solutions of plane Couette flow. https://doi.org/10.1103/physreve.100.031102

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