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ON MODELLING THE TRANSITION TO TURBULENCE IN PIPE FLOW

Part of: Turbulence

Published online by Cambridge University Press:  11 July 2017

LAWRENCE K. FORBES  and
MICHAEL A. BRIDESON
LAWRENCE K. FORBES*
Affiliation:
School of Mathematics and Physics, University of Tasmania, Tasmania, Australia email larry.forbes@utas.edu.au and michael.brideson@utas.edu.au
MICHAEL A. BRIDESON
Affiliation:
School of Mathematics and Physics, University of Tasmania, Tasmania, Australia email larry.forbes@utas.edu.au and michael.brideson@utas.edu.au
*
✉larry.forbes@utas.edu.au
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Abstract

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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.

Keywords

circular pipelinearizationPoiseuille flowReiner–Rivlin equationsstability analysistransition to turbulence

MSC classification

Primary: 76F06: Transition to turbulence
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 1 , July 2017 , pp. 1 - 34
Copyright
© 2017 Australian Mathematical Society 

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