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ON TURBULENCE MODELLING AND THE TRANSITION FROM LAMINAR TO TURBULENT FLOW

Part of: Foundations, constitutive equations, rheology Turbulence

Published online by Cambridge University Press:  09 October 2014

LAWRENCE K. FORBES
LAWRENCE K. FORBES*
Affiliation:
School of Mathematics and Physics, University of Tasmania, Tasmania 7004, Australia email [email protected]
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Abstract

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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.

Keywords

fluid turbulenceflow stabilitynonlinear viscositynon-Newtonian behaviourturbulence modelling

MSC classification

Secondary: 76F02: Fundamentals 76A02: Foundations of fluid mechanics
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 1 , July 2014 , pp. 28 - 47
Copyright
Copyright © 2014 Australian Mathematical Society 

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