A doubly-localized equilibrium solution of plane Couette flow
arXiv:1404.2887 · doi:10.1017/jfm.2014.285
Abstract
We present an equilibrium solution of plane Couette flow that is exponentially localized in both the spanwise and streamwise directions. The solution is similar in size and structure to previously computed turbulent spots and localized, chaotically wandering edge states of plane Couette flow. A linear analysis of dominant terms in the Navier-Stokes equations shows how the exponential decay rate and the wall-normal overhang profile of the streamwise tails are governed by the Reynolds number and the dominant spanwise wavenumber. Perturbations of the solution along its leading eigenfunctions cause rapid disruption of the interior roll-streak structure and formation of a turbulent spot, whose growth or decay depends on the Reynolds number and the choice of perturbation.
arXiv comment11 pages, 5 figures. Discussion of symmetries expanded to explain angle-bracket notation and antisymmetries of eigenfunctions. More explicit discussion of the determination of the dominant spanwise wavenumber of the tails
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