Complexity of the laminar-turbulent boundary in pipe flow

Abstract

Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of states that separate laminar and turbulent regions of the state space. In addition, some studies determined invariant solutions that reside on this edge. In this paper, we study the unstable manifold of one such solution with the aid of continuous symmetry-reduction, which we formulate here for the first time for the simultaneous quotiening of axial and azimuthal symmetries. Upon our investigation of the unstable manifold, we discover a previously unknown traveling wave solution on the laminar-turbulent boundary with a relatively complex structure. By means of low-dimensional projections, we visualize different dynamical paths that connect these solutions to the turbulence. Our numerical experiments demonstrate that the laminar-turbulent boundary exhibits qualitatively different regions whose properties are influenced by the nearby invariant solutions.

arXiv comment15 pages, 11 figures

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Cited by in corpus (10)

• Coarse graining the state space of a turbulent flow using periodic orbits
• Symmetry-reduced Dynamic Mode Decomposition of Near-wall Turbulence
• Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the Kuramoto-Sivashinsky system
• Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow
• Inferring symbolic dynamics of chaotic flows from persistence
• Linear feedback control of invariant solutions in channel flow
• Upper edge of chaos and the energetics of transition in pipe flow
• A linear system for pipe flow stability analysis allowing for boundary condition modifications
• A traveling wave bifurcation analysis of turbulent pipe flow
• Crises and chaotic scattering in hydrodynamic pilot-wave experiments