## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Dynamical system approach and attracting manifolds in $K$-$\varepsilon$ model of turbulent jet

D.V. Strunin

#### 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 15, Number 5 (2008), 935-946.

Dates
First available in Project Euclid: 5 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1228486417

Mathematical Reviews number (MathSciNet)
MR2484142

Zentralblatt MATH identifier
1165.37033

#### Citation

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.https://projecteuclid.org/euclid.bbms/1228486417