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On turbulence modelling and the transition from laminar to turbulent flow


Forbes, LK, On turbulence modelling and the transition from laminar to turbulent flow, The ANZIAM Journal, 56, (1) pp. 28-47. ISSN 1446-1811 (2014) [Refereed Article]



Copyright Statement

Copyright 2014 Australian Mathematical Society

DOI: doi:10.1017/S1446181114000224


Fluid turbulence is often modelled using equations derived from the Navier–Stokes equations, perhaps with some semi-heuristic closure model for the turbulent viscosity. This paper considers a possible alternative hypothesis. It is argued that regarding turbulence as a manifestation of non-Newtonian behaviour may be a viewpoint of at least comparable validity. For a general description of nonlinear viscosity in a Stokes fluid, it is shown that the flow patterns are indistinguishable from those predicted by the Navier–Stokes equation in one- or two-dimensional geometry, but that fully three-dimensional flows differ markedly. The stability of linearized plane Poiseuille flow to three-dimensional disturbances is then considered, in a Tollmien–Schlichting formulation. It is demonstrated that the flow may become unstable at significantly lower Reynolds numbers than those expected from Navier–Stokes theory. Although similar results are known in sections of the rheological literature, the present work attempts to advance the philosophical viewpoint that turbulence might always be regarded as a non-Newtonian effect, to a degree that is dependent only on the particular fluid in question. Such an approach could give a more satisfactory account of the underlying physics.

Item Details

Item Type:Refereed Article
Keywords:fluid turbulence, non-Newtonian behaviour, stability, flow stability, nonlinear viscosity, turbulence modelling
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Forbes, LK (Professor Larry Forbes)
ID Code:97606
Year Published:2014
Funding Support:Australian Research Council (DP140100094)
Web of Science® Times Cited:3
Deposited By:Mathematics and Physics
Deposited On:2015-01-02
Last Modified:2017-11-01
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