University Of Tasmania
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On turbulence modelling and the transition from laminar to turbulent flow

journal contribution
posted on 2023-05-18, 06:06 authored by Lawrence ForbesLawrence Forbes
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.


Australian Research Council


Publication title

The ANZIAM Journal








School of Natural Sciences


Australian Mathematics Publ Assoc Inc

Place of publication

Mathematics Dept Australian National Univ, Canberra, Australia, Act, 0200

Rights statement

Copyright 2014 Australian Mathematical Society

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in the mathematical sciences