Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 15, Number 5 (2008), 935-946.
Dynamical system approach and attracting manifolds in $K$-$\varepsilon$ model of turbulent jet
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.
Bull. Belg. Math. Soc. Simon Stevin Volume 15, Number 5 (2008), 935-946.
First available in Project Euclid: 5 December 2008
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37L25: Inertial manifolds and other invariant attracting sets 37N10: Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]
Strunin, D.V. Dynamical system approach and attracting manifolds in $K$-$\varepsilon$ model of turbulent jet. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 5, 935--946. http://projecteuclid.org/euclid.bbms/1228486417.