## Dynamical system approach and attracting manifolds in $$k$$-$$\varepsilon$$ model of turbulent jet.(English)Zbl 1165.37033

The $$k$$-$$\varepsilon$$ model of expanding turbulence shaped as a plane jet is analysed. Profiles of energy, dissipation rate and velocity across the jet are sought in the form of power series. The series coefficients satisfy a nonlinear dynamical system with a few slow variables. Based on these variables, an attractor in the form of a system of algebraic equations linking fast and slow variables is found. The approach allows to naturally define the position of the front of turbulence.

### MSC:

 37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology 76F60 $$k$$-$$\varepsilon$$ modeling in turbulence 76F20 Dynamical systems approach to turbulence 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing

### Keywords:

nonlinear diffusion; dynamical system; attractor
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