Stable manifolds and the transition to turbulence in pipe flow

2008/01/31 by D. Viswanath, D. VISWANATH, P. Cvitanovic +1
Engineering · Physics and Astronomy · #Aerodynamics and Acoustics in Jet Flows #Flow (mathematics) #Fluid Dynamics and Thin Films #Fluid Dynamics and Turbulent Flows #Laminar flow #Laminar-turbulent transition #Open-channel flow #Pipe flow #Plug flow #Turbulence #Vector field #physics.flu-dyn

paper · pdf · doi:10.1017/s0022112009006041

published as Journal of Fluid Mechanics, vol. 627 (2009), p. 215-233

arxiv created 2008/12/24 · openalex publication_date 2009/05/12 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Lower branch travelling 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.

Citations

• Lower Branch Coherent States in Shear Flows: Transition and Control
• Fractal Stability Border in Plane Couette Flow
• Recurrence of travelling waves in transitional pipe flow
• Scaling of the Turbulence Transition Threshold in a Pipe
• Asymmetric, Helical, and Mirror-Symmetric Traveling Waves in Pipe Flow
• Statistical analysis of coherent structures in transitional pipe flow
• Coherent Motions in the Turbulent Boundary Layer