SPECTRAL CHARACTERISTICS OF AN INCOMPRESSIBLE FLUID FLOW IN TURBULENT BOUNDARY LAYERS
The aim is to study a model of a developed turbulent flow of an incompressible fluid in a boundary layer on a plate. The study is based on the analysis of the Navier-Stokes equations describing the behaviour of Tollmien-Schlichting wave amplitudes in a single-mode approximation. Methodology. A weakly nonlinear version of the wave model of a developed turbulent boundary layer is considered. The dispersion characteristics of the waves of the least damped mode are determined, and the conditions of multiple three-wave resonance of this mode of Tollmien-Schlichting waves are analyzed. Equations for the coherent part are obtained using the many-scale method. Results. In the discrete representation of the coherent structure, it is shown that the sum of the squares of the moduli of the wave amplitudes in the state of multiple three-wave resonance, multiplied by real weight factors, is an invariant of the original dynamical system. Research implications. The invariant of the dynamic system is normalized to unity, and the Birkhoff-Khinchin theory is formulated.