On modelling the transition to turbulence in pipe flow

Lawrence K. Forbes, Michael A. Brideson

Abstract


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.

doi:10.1017/S1446181117000256

Keywords


circular pipe, linearization, Poiseuille flow, Reiner–Rivlin equations, stability analysis, transition to turbulence.



DOI: http://dx.doi.org/10.21914/anziamj.v59i0.11292



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.