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Slug genesis in cylindrical pipe flow. (English) Zbl 1205.76126
Summary: Transition to uniform turbulence in cylindrical pipe flow occurs experimentally via the spatial expansion of isolated coherent structures called ‘slugs’, triggered by localized finite-amplitude disturbances. We study this process numerically by examining the preferred route in phase space through which a critical disturbance initiates a ‘slug’. This entails first identifying the relative attractor - ‘edge state’ - on the laminar-turbulent boundary in a long pipe and then studying the dynamics along its low-dimensional unstable manifold, leading to the turbulent state. Even though the fully turbulent state delocalizes at \(Re \approx 2300\), the edge state is found to be localized over the range \(Re = 2000-6000\), and progressively reduces in both energy and spatial extent as \(Re\) is increased. A key process in the genesis of a slug is found to be vortex shedding via a Kelvin-Helmholtz mechanism from wall-attached shear layers quickly formed at the edge state’s upstream boundary. Whether these shedded vortices travel on average faster or slower downstream than the developing turbulence determines whether a puff or a slug (respectively) is formed. This observation suggests that slugs are out-of-equilibrium puffs which therefore do not co-exist with stable puffs.

MSC:
76F06 Transition to turbulence
76M20 Finite difference methods applied to problems in fluid mechanics
76M22 Spectral methods applied to problems in fluid mechanics
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