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TsAGI Science Journal

ISSN Print: 1948-2590
ISSN Online: 1948-2604

TsAGI Science Journal

DOI: 10.1615/TsAGISciJ.2015013391
pages 739-758

MODEL PRESENTATION OF THE COHERENT STRUCTURE IN THE DEVELOPED TURBULENT BOUNDARY LAYER

Vladimir Alekseevich Zharov
Central Aerohydrodynamic Institute (TsAGI), Zhukovsky str. 1, Zhukovsky, 140180, Russia

ABSTRACT

A weakly nonlinear variant of the wave model of the developed turbulent boundary layer is considered. The dispersion properties of the least-damping Tollmien-Schlichting waves are determined, and the conditions for the existence of the three-wave resonance are analyzed. Equations for the coherent and stochastic parts of fluctuations are derived on the basis of a multiscale method. In the discrete presentation of the coherent structure, it is demonstrated that the sum of the squared absolute values of the wave amplitudes in the three-wave resonance multiplied by the real weight factors is an invariant of the original dynamic system. The range of positive values of the weight factors in the wave space is found. The dynamics of the wave system in this range is finite. Reduced equations for the coherent and stochastic parts of the flow are obtained, a scaling law is formulated, and the structure of the Reynolds stress tensor is analyzed.


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