Stable Manifolds and the Transition to Turbulence in Pipe Flow

Details Stable Manifolds and the Transition to Turbulence in Pipe Flow Stable Manifolds and the Transition to Turbulence in Pipe Flow

2008-01-12

arxiv.org/abs/0801.1918v2

Physics

Fluid Dynamics

Scientific paper

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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