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On modelling the transition to turbulence in pipe flow

Forbes, LK ORCID: 0000-0002-9135-3594 and Brideson, MA ORCID: 0000-0001-7547-5084 2017 , 'On modelling the transition to turbulence in pipe flow' , ANZIAM Journal, vol. 59, no. 1 , pp. 1-34 , doi: 10.1017/S1446181117000256.

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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.

Item Type: Article
Authors/Creators:Forbes, LK and Brideson, MA
Keywords: transition to turbulence, stability analysis, Reiner-Rivlin equations, Poiseuille flow, linearization, circular pipe
Journal or Publication Title: ANZIAM Journal
Publisher: Australian Mathematics Publ Assoc Inc
ISSN: 1446-1811
DOI / ID Number: 10.1017/S1446181117000256
Copyright Information:

Copyright 2017 Australian Mathematical Society

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