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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