English

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

Fluid Dynamics 2019-09-18 v1 Pattern Formation and Solitons

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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Cite

@article{arxiv.1906.06277,
  title  = {The origin of localized snakes-and-ladders solutions of plane Couette flow},
  author = {Matthew Salewski and John F. Gibson and Tobias M. Schneider},
  journal= {arXiv preprint arXiv:1906.06277},
  year   = {2019}
}

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5 pages