Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics

Roberts, A. J. (2003) Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics. In: Nonlinear dynamics from lasers to butterflies: selected lectures from the 15th Canberra International Physics Summer School. Lecture Notes in Complex Systems (1). World Scientific, pp. 257-313. ISBN 9789812791252


Consider briefly the equations of fluid dynamics — they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow — whereas in applications we want to deal with a description of just that which is interesting. In a wide variety of situations, simple approximate models are needed to perform practical simulations and make forecasts. I overview the derivation, from a mathematical description of the detailed dynamics, to accurate and complete low-dimensional models of the interesting dynamics in a system. The development of centre manifold theory and associated techniques puts this modelling process on a firm basis. The geometric viewpoint of dynamical systems theory greatly enriches our approach.

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Item Type: Book Chapter (Commonwealth Reporting Category B)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author's version not held.
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 20 Apr 2010 10:31
Last Modified: 21 Sep 2016 03:02
Uncontrolled Keywords: dynamical systems; centre manifold theory; fluid mechanics
Fields of Research : 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
09 Engineering > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
URI: http://eprints.usq.edu.au/id/eprint/7524

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