2010/07/21 by Sergey G. Chefranov, Chefranov, Sergey G., Alexander G. Chefranov +1
Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1007.3586
arxiv created 2010/07/21 · arxiv updated 2010/07/22
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 bi-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.