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.


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
Full Text: Euclid