phmathВестник Государственного университета просвещения. Серия: Физика-МатематикаBulletin of Federal State University of Education. Series: Physics and Mathematics2949-50832949-5067Federal State University of Education10.18384/2310-7251-2021-4-75-85phmath-97Research ArticleФИЗИКАPHYSICSТурбулентная статистика с точки зрения когерентной структуры в пограничном слоеTurbulent Statistics in terms of coherent structure in the boundary layerСелимР. С.SelimS. S.selim.rs@phystech.eduМосковский физико-технический институт(национальный исследовательский университет); Университет ТантаРоссияMoscow Institute of Physics and Technology (National Research University); Tanta UniversityRussian Federation202115022022047585Copyright © Селим Р.С., 20222022Селим Р.С.Selim S.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.physmathmgou.ru/jour/article/view/97

Цель работы: исследование эргодичности динамической системы уравнений для амплитуд набора волн Толлмина-Шлихтинга, с помощью которых аппроксимируется стохастическое поведение турбулентных пульсаций, и проведение сравнения с экспериментом пульсационных характеристик развитого турбулентного пограничного слоя при нулевом градиенте давления в рамках волноводной модели. Процедура и методы. В работе использована машинная аналитика и комплекс прикладных программ MATHEMATICA. Ряд результатов получен на основе теории динамических систем. Результаты. Показана сходимость временных средних и средних по пространству. Кроме того, продемонстрирована хорошая сходимость теоретических результатов, обусловленных когерентной составляющей, с экспериментальными. Теоретическая и практическая значимость. Показана применимость волноводной модели для изучения статистики пульсаций скорости потока в пограничном слое для несжимаемой жидкости при нулевом градиенте давления.

Aim of study: investigation the ergodicity of a dynamical system for a set equations of amplitudes Tollmien-Schlichting waves, with the help of approximation stochastic behavior of turbulent pulsations, and comparison the pulsation characteristics of a developed turbulent boundary layer in terms of the waveguide model with experiment at zero pressure gradient. Methodology. The paper uses machine analytics and a complex of MATHEMATICA application programs. A number of results are obtained on the basis of dynamical systems theory. Results. The convergence of time averages and phase averages is shown. In addition, a good convergence of the theoretical results due to the coherent component with the experimental results has been demonstrated. Research implication.The applicability of the waveguide model for studying the statistics of flow velocity pulsations in the turbulent boundary layer for an incompressible fluid at zero pressure gradient is shown.

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The authors declare that there are no conflicts of interest present.