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On turbulence modelling and the transition from laminar to turbulent flow
Citation
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
Abstract
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 |
| Downloads: | 100 View Download Statistics |
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