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  • ON MODELLING THE TRANSITION TO TURBULENCE IN PIPE FLOW

  • Part of
  • LAWRENCE K. FORBES, MICHAEL A. BRIDESON
  • Journal:
    The ANZIAM Journal / Volume 59 / Issue 1 / July 2017
    Published online by Cambridge University Press:
    11 July 2017, pp. 1-34
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  • As a possible model for fluid turbulence, a Reiner–Rivlin-type equation is used to study Poiseuille–Couette flow of a viscous fluid in a rotating cylindrical pipe. The equations of motion are derived in cylindrical coordinates, and small-amplitude perturbations are considered in full generality, involving all three velocity components. A new matrix-based numerical technique is proposed for the linearized problem, from which the stability is determined using a generalized eigenvalue approach. New results are obtained in this cylindrical geometry, which confirm and generalize the predictions of previous recent studies. A possible mechanism for the transition to turbulent flow is discussed.