2008/08/13 by Jonathan Halcrow, John F. Gibson, J. F. Gibson +2
Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Bifurcation #Bifurcation theory #Classical mechanics #Connection (principal bundle) #Couette flow #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometry #Heteroclinic bifurcation #Heteroclinic cycle #Heteroclinic orbit #Homoclinic orbit #Laminar flow #Mathematics #Mechanics #Nonlinear system #Phase Equilibria and Thermodynamics #Physics #Plane (geometry) #Plant Water Relations and Carbon Dynamics #Reynolds number #Turbulence #physics.flu-dyn
paper · pdf · doi:10.1017/s0022112008005065
11 pages, 4 figures, to be submitted to Journal of Fluid Mechanics
arxiv created 2008/08/13 · openalex publication_date 2009/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Plane Couette flow transitions to turbulence at Re ≈ 325 even though the laminar solution with a linear profile is linearly stable for all Re (Reynolds number). One starting point for understanding this subcritical transition is the existence of invariant sets in the state space of the Navier–Stokes equation, such as upper and lower branch equilibria and periodic and relative periodic solutions, that are distinct from the laminar solution. This article reports several heteroclinic connections between such objects and briefly describes a numerical method for locating heteroclinic connections. We show that the nature of streaks and streamwise rolls can change significantly along a heteroclinic connection.