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Transition to turbulence from plane Couette flow


Forbes, LK, Transition to turbulence from plane Couette flow, The ANZIAM Journal, 57, (2) pp. 89-113. ISSN 1446-1811 (2015) [Refereed Article]

Copyright Statement

Copyright 2015 Australian Mathematical Society

DOI: doi:10.1017/S1446181115000176


Modelling fluid turbulence is perhaps one of the hardest problems in Applied Mathematics. In a recent paper, the author argued that the classical Navier–Stokes equation is not sufficient to describe the transition to turbulence, but that a Reiner–Rivlin type equation is needed instead. This is explored here for the simplest of all viscous fluid flows, the Couette flow, which is a simple shear between two moving plates. It is found that at high wavenumbers, the transition to unstable flow at the critical Reynolds number is characterized by a large number of eigenvalues of the Orr–Sommerfeld equation moving into the unstable zone essentially simultaneously. This would generate high-dimensional chaos almost immediately, and is a suggested mechanism for the transition to turbulence. Stability zones are illustrated for the flow, and a simple asymptotic solution confirms some of the features of these numerical results.

Item Details

Item Type:Refereed Article
Keywords:viscous fluid, transition flows, turbulence, stability analysis, Couette flow, instability, nonNewtonian effects
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:106702
Year Published:2015
Funding Support:Australian Research Council (DP140100094)
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2016-02-17
Last Modified:2017-11-01

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