Dynamical system approach and attracting manifolds in K-epsilon model of turbulent jet

Strunin, D. V. (2008) Dynamical system approach and attracting manifolds in K-epsilon model of turbulent jet. Bulletin of the Belgian Mathematical Society: Simon Stevin, 15 (5). pp. 935-946. ISSN 1370-1444

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Abstract

We consider the K-epsilon model describing an expansion of a free turbulent jet. Due to the nonlinear nature of turbulent diffusion the turbulent area has a sharp boundary. We seek solutions for the energy, dissipation and momentum as power series in spatial coordinate across the jet with time-dependent coefficients. The coefficients obey a dynamical system with clearly identifiable slow and fast variables. The system is not in a standard form, which excludes rigorous methods of analysis such as centre manifold methods. We put forward a hypothesis that there exists an attracting invariant manifold for trajectories based on a few slow variables. The hypothesis is supported numerically.

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Item Type:	Article (Commonwealth Reporting Category C)
Refereed:	Yes
Item Status:	Live Archive
Additional Information:	This is the publisher reprint version of the paper. Author retains copyright. Deposited with blanket permission of the publisher.
Faculty / Department / School:	Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited:	14 Jul 2009 12:43
Last Modified:	19 Jan 2015 23:27
Uncontrolled Keywords:	turbulent jet; k-epsilon model; dynamical system
Fields of Research :	09 Engineering > 0915 Interdisciplinary Engineering > 091508 Turbulent Flows 09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics 01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
Socio-Economic Objective:	E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI:	http://eprints.usq.edu.au/id/eprint/5079

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