On modelling the transition to turbulence in pipe flow

Authors

  • Lawrence K. Forbes School of Mathematics and Physics University of Tasmania
  • Michael A. Brideson School of Mathematics and Physics University of Tasmania

DOI:

https://doi.org/10.21914/anziamj.v59i0.11292

Keywords:

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

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

Author Biography

Lawrence K. Forbes, School of Mathematics and Physics University of Tasmania

Professor of Mathematics School of Mathematics and Physics

Published

2017-09-05

Issue

Section

Articles for Printed Issues