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Mathematical Modeling of Incompressible Fluid Flow in Turbulent Boundary Layers
https://orcid.org/http://orcid.org/0000-0001-9508-8620
https://orcid.org/http://orcid.org/0000-0003-2769-0833
https://orcid.org/http://orcid.org/0000-0001-7288-5475
This paper considers, in the framework of the model of the developed turbulent flow of an incompressible fluid over a plate in a boundary layer. The problem investigated the formulation of amplitudes in a single-mode approximation through a weakly nonlinear version of the wave model. The dispersion characteristics of the least damping wave mode are deduced by the Chebyshev collocation method, and then exploited to derive the curve of three-wave resonance. Equation for the coherent part is obtained by using the multi-scale method. The conditions for multiple 3-wave resonance of Tollmien-Schlichting modes are analyzed, to deduce the dynamical system of the model. In the state of multiple 3-wave resonance, this system is examined for solutions corresponding to real positive weight factors. It is observed that, in a discrete representation of the coherent structure, the sum squares of modules, wave amplitudes, is an invariant of the original dynamical system. This invariant is normalized to unity, in order to use the Birkhoff - Khinchin theorem. The result of averaging squares of harmonic, and sub harmonic amplitudes by time, and over a representative set of initial data are investigated.
Mathematical Modeling of Incompressible Fluid Flow in Turbulent Boundary Layers
https://orcid.org/http://orcid.org/0000-0001-9508-8620
https://orcid.org/http://orcid.org/0000-0003-2769-0833
https://orcid.org/http://orcid.org/0000-0001-7288-5475
This paper considers, in the framework of the model of the developed turbulent flow of an incompressible fluid over a plate in a boundary layer. The problem investigated the formulation of amplitudes in a single-mode approximation through a weakly nonlinear version of the wave model. The dispersion characteristics of the least damping wave mode are deduced by the Chebyshev collocation method, and then exploited to derive the curve of three-wave resonance. Equation for the coherent part is obtained by using the multi-scale method. The conditions for multiple 3-wave resonance of Tollmien-Schlichting modes are analyzed, to deduce the dynamical system of the model. In the state of multiple 3-wave resonance, this system is examined for solutions corresponding to real positive weight factors. It is observed that, in a discrete representation of the coherent structure, the sum squares of modules, wave amplitudes, is an invariant of the original dynamical system. This invariant is normalized to unity, in order to use the Birkhoff - Khinchin theorem. The result of averaging squares of harmonic, and sub harmonic amplitudes by time, and over a representative set of initial data are investigated.
Mathematical Modeling of Incompressible Fluid Flow in Turbulent Boundary Layers
https://orcid.org/http://orcid.org/0000-0001-9508-8620
https://orcid.org/http://orcid.org/0000-0003-2769-0833
https://orcid.org/http://orcid.org/0000-0001-7288-5475
This paper considers, in the framework of the model of the developed turbulent flow of an incompressible fluid over a plate in a boundary layer. The problem investigated the formulation of amplitudes in a single-mode approximation through a weakly nonlinear version of the wave model. The dispersion characteristics of the least damping wave mode are deduced by the Chebyshev collocation method, and then exploited to derive the curve of three-wave resonance. Equation for the coherent part is obtained by using the multi-scale method. The conditions for multiple 3-wave resonance of Tollmien-Schlichting modes are analyzed, to deduce the dynamical system of the model. In the state of multiple 3-wave resonance, this system is examined for solutions corresponding to real positive weight factors. It is observed that, in a discrete representation of the coherent structure, the sum squares of modules, wave amplitudes, is an invariant of the original dynamical system. This invariant is normalized to unity, in order to use the Birkhoff - Khinchin theorem. The result of averaging squares of harmonic, and sub harmonic amplitudes by time, and over a representative set of initial data are investigated.
Mathematical Modeling of Incompressible Fluid Flow in Turbulent Boundary Layers
Lecture Notes in Civil Engineering
Mottaeva, Angela (editor) / Zharov, Vladimir (author) / Lipatov, Igor (author) / Selim, Ramy (author)
International Scientific Conference on Architecture and Construction ; 2020
2020-12-24
15 pages
Article/Chapter (Book)
Electronic Resource
English
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