Life on the edge: subcritical pipe flow transition as a spectral submanifold

Subcritical pipe flow transition has received a great deal of attention over the past decades, as it constitutes a quintessential bifurcation process between two metastable fluid states: the laminar and turbulent solutions. Coherent lower-branch structures, forming flow states that facilitate between these two attracting equilibria, have been proposed that together form an edge manifold in phase space separating relaminarizing from transitioning perturbations. Typically, direct numerical simulations or low-dimensional model equations have been used to study this edge manifold with bisection methods. In the article by Kaszás & Haller (J. Fluid Mech., vol. 979, 2024, A48), an effective nonlinear invariant-manifold technique has been applied to extract a low-dimensional, global representation of the phase-space dynamics directly from simulation data. It allows the computation of the intersection of the edge manifold with a low-dimensional surface that is strikingly accurate in predicting the long-term dynamics of perturbations about the lower-branch solution and thus provides an accessible parameterization of the edge manifold for subcritical pipe flow transition.