Stable Manifolds and the Transition to Turbulence in Pipe Flow

Abstract

Lower-branch traveling waves and equilibria computed in pipe flow and other shear flows appear intermediate between turbulent and laminar motions. We take a step towards connecting these lower-branch solutions to transition by deriving a numerical method for finding certain special disturbances of the laminar flow in a short pipe. These special disturbances cause the disturbed velocity field to approach the lower-branch solution by evolving along its stable manifold. If the disturbance were slightly smaller, the flow would relaminarize, and if slightly larger, it would transition to a turbulent state.

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Cited by in corpus (7)

• Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos
• An optimisation approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar
• Exact coherent states and connections to turbulent dynamics in minimal channel flow
• Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow
• Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow
• Stably stratified exact coherent structures in shear flow: the effect of Prandtl number
• Dynamics of a Data-Driven Low-Dimensional Model of Turbulent Minimal Pipe Flow