Salewski M, Gibson JF, Schneider TM. Origin of localized snakes-and-ladders solutions of plane Couette flow.
Phys Rev E 2019;
100:031102. [PMID:
31640040 DOI:
10.1103/physreve.100.031102]
[Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2019] [Indexed: 11/07/2022]
Abstract
Spatially localized invariant 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 [Schneider, Gibson, and Burke, Phys. Rev. Lett. 104, 104501 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.104501]. 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 close connection between pattern-formation theory and Navier-Stokes flow.
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