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December 2008 Dynamical system approach and attracting manifolds in $K$-$\varepsilon$ model of turbulent jet
D.V. Strunin
Bull. Belg. Math. Soc. Simon Stevin 15(5): 935-946 (December 2008). DOI: 10.36045/bbms/1228486417

Abstract

We consider the $K$-$\varepsilon$ 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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D.V. Strunin. "Dynamical system approach and attracting manifolds in $K$-$\varepsilon$ model of turbulent jet." Bull. Belg. Math. Soc. Simon Stevin 15 (5) 935 - 946, December 2008. https://doi.org/10.36045/bbms/1228486417

Information

Published: December 2008
First available in Project Euclid: 5 December 2008

zbMATH: 1165.37033
MathSciNet: MR2484142
Digital Object Identifier: 10.36045/bbms/1228486417

Subjects:
Primary: 37L25 , 37N10

Keywords: attractor , dynamical system , Nonlinear diffusion

Rights: Copyright © 2008 The Belgian Mathematical Society

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Vol.15 • No. 5 • December 2008
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