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Instability in Pipe Flow



David Cotrell, Geoffrey B. McFadden, W. E. Alley, B. J. Alder


An axisymmetric linear stability analysis is carried out for flow driven by an axial pressure gradient in a pipe with axisymmetric and axially-periodic radius variation (i.e., axial corrugation). The steady base flow is assumed to be axisymmetric and axially-periodic with a specified radius variation wavelength and amplitude, and the azimuthal velocity component is taken to be zero. Results show that for a suffciently large Reynolds number, the onset of vortex formation is observed in the bulge, however, the flow is linearly stable both above and below this Reynolds number. Further increase of the Reynolds number leads to a second transition to an unsteady secondary flow having different axial wavenumber than the wall periodicity. This transition Reynolds number is monotonically increasing with decreasing radius variation amplitude and extrapolates (at infinite Reynolds number) to a nonzero amplitude value nearly identical to the threshold amplitude.
Journal of Fluid Mechanics


critical Reynolds number, hydrodynamic stability, linear stability, Navier-Stokes equations, spatially-modulated pipe flow


Cotrell, D. , McFadden, G. , Alley, W. and Alder, B. (2008), Instability in Pipe Flow, Journal of Fluid Mechanics, [online], (Accessed July 15, 2024)


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Created January 15, 2008, Updated January 27, 2020