2014/04/30 by Evan Brand, John F. Gibson, J. F. Gibson · 52 citations
Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Classical mechanics #Couette flow #Eigenfunction #Eigenvalues and eigenvectors #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Geometry #Mathematics #Mechanics #Optics #Perturbation (astronomy) #Physics #Plane (geometry) #Plant Water Relations and Carbon Dynamics #Reynolds number #Streak #Taylor–Couette flow #Turbulence #Wavenumber #msc:76E05 #msc:76E30 #physics.flu-dyn
paper · pdf · doi:10.1017/jfm.2014.285
published in Journal of Fluid Mechanics 750 (Cambridge University Press) · 11 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
arxiv created 2014/05/21 · openalex publication_date 2014/06/05 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.