Round Pipe Flow Linear Stability Famous Century-Old Paradox Resolving and the New Boundary Layer Turbulence Arising Theory

Details Round Pipe Flow Linear Stability Famous Century-Old Paradox Resolving and the New Boundary Layer Turbulence Arising Theory Round Pipe Flow Linear Stability Famous Century-Old Paradox Resolving and the New Boundary Layer Turbulence Arising Theory

2010-07-07

arxiv.org/abs/1007.1097v1

Physics

Fluid Dynamics

Scientific paper

For Gagen-Poiseuille flow, we show that exponential instability (to extremely small, axially symmetric disturbances represented by Galerkin's approximation) is possible only if there exists conditionally periodic variability of the disturbances along the pipe axis when the threshold Reynolds number depends on the ratio of two longitudinal periods. Absolute minimum (for) is obtained that corresponds to the observed conditions of transition from the laminar resistance law to the turbulent one and Tollmien-Schlichting waves exciting in the boundary layer.

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