Roberts, A. J. (2003) Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics. In: Ball, Rowena and Akhmediev, Nial, (eds.) 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
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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.
|Item Type:||Book Chapter (Commonwealth Reporting Category B)|
|Additional Information:||Author's version not held. Print copy not held in the USQ Library.|
|Uncontrolled Keywords:||dynamical systems; centre manifold theory; fluid mechanics|
|Fields of Research (FOR2008):||02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics|
09 Engineering > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics
|Socio-Economic Objective (SEO2008):||E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering|
|Deposited On:||20 Apr 2010 20:31|
|Last Modified:||29 Jun 2012 09:46|
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