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{1228486417,
author = {Strunin, D.V.},
title = {Dynamical system approach and attracting manifolds in $K$-$\varepsilon$ model of turbulent jet},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {15},
number = {1},
year = {2008},
pages = { 935-946},
language = {en},
url = {http://dml.mathdoc.fr/item/1228486417}
}
Strunin, D.V. Dynamical system approach and attracting manifolds in $K$-$\varepsilon$ model of turbulent jet. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp. 935-946. http://gdmltest.u-ga.fr/item/1228486417/