Spatially localized solutions of plane Couette flow

ORAL

Abstract

We examine spatially localized solutions of plane Couette flow: traveling waves and equilibria with finite spanwise extent and periodic streamwise structure. We show that these solutions exist over a wide range of Reynolds numbers, from Re=170 to at least Re=4000, and demonstrate a relationship between the streamwise periodicity of a solution and the range of Reynolds number over which it appears. Some solutions display a diagonal or winding symmetry, suggestively similar to the diagonal bands of structure observed in large-scale simulations by Tuckermann and Barkley.

*Partially supported by NSF grant DMS-0807574.

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Authors

  • John Gibson

    • University of New Hampshire

  • Tobias M. Schneider

    • School of Engineering and Applied Sciences, Harvard University
    • Harvard University

  • John Burke

    • Boston University