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    Kerswell, R R 2005. Recent progress in understanding the transition to turbulence in a pipe. Nonlinearity, Vol. 18, Issue. 6, p. R17.


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  • Journal of Fluid Mechanics, Volume 457
  • April 2002, pp. 339-376

The temporal evolution of neutral modes in the impulsively started flow through a circular pipe and their connection to the nonlinear stability of Hagen–Poiseuille flow

  • ANDREW G. WALTON (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112001007674
  • Published online: 01 April 2002
Abstract

The linear stability of the impulsively started flow through a pipe of circular cross-section is studied at high Reynolds number R. A crucial non-dimensional time of O(R7/9) is identified at which the disturbance acquires internal flow characteristics. It is shown that even if the disturbance amplitude at this time is as small as O(R−22/27) the subsequent evolution of the perturbation is nonlinear, although it can still be followed analytically using a multiple-scales approach. The amplitude and wave speed of the nonlinear disturbance are calculated as functions of time and we show that as t → ∞, the disturbance evolves into the long-wave limit of the neutral mode structure found by Smith & Bodonyi in the fully developed Hagen–Poiseuille flow, into which our basic flow ultimately evolves. It is proposed that the critical amplitude found here forms a stability boundary between the decay of linear disturbances and ‘bypass’ transition, in which the fully developed state is never attained.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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