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Vortices in the Prandtl boundary layer induced by irregularities on a plate
Russian Journal of Mathematical Physics. 2015. Vol. 22. No. 2. P. 161-173.
A fluid flow along a plate with small irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure, i.e., both a thin boundary layer and the classical Prandtl boundary layer are present. It is proved that the solution of the boundary-value problem thus obtained exists and is unique in the Prandtl boundary layer, and the stability of the solution is investigated at large times. The results of numerical modeling are given. Supported by the Basic Research Program of the National Research University “Higher School of Economics.” © 2015, Pleiades Publishing, Ltd.
Danilov V., Gaydukov R., Mathematical notes 2015 Vol. 98 No. 4 P. 561-571
We consider the problem of a viscous incompressible fluid flow along a flat plate with a small solitary perturbation (of hump, step, or corner type) for large Reynolds numbers. We obtain an asymptotic solution in which the boundary layer has a double-deck structure. ...
Added: September 27, 2015
Gaydukov R., Danilov V., Наноструктуры. Математическая физика и моделирование 2016 Т. 15 № 1 С. 5-102
We study the existence conditions for a double-deck structure of a boundary layer in typical problems of incompressible fluid flow along surfaces with small irregularities (periodic or localized) for large Reynolds number. We obtain characteristic scales (a power of a small parameter included in a solution) which lead to the double-deck structure, and we obtain ...
Added: September 27, 2016
Gaydukov R. K., European Journal of Mechanics - B/Fluids 2017 Vol. 66 P. 102-108
We consider the problem of a viscous compressible subsonic fluid flow along a flat plate with small periodic irregularities on the surface for large Reynolds numbers. We obtain a formal asymptotic solution with double-deck structure of the boundary layer. We present the results of numerical simulation of flow in the thin boundary layer (i.e., in ...
Added: July 9, 2017
Gaydukov R. K., Borisov D. I., Mathematical notes 2016 Vol. 99 No. 5 P. 636-642
A fluid flow along a semi-infinite plate with small periodic irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure: a thin boundary layer (“lower deck”) and a classical Prandtl boundary layer (“upper deck”). The aim of this paper is to prove the existence and uniqueness of the ...
Added: May 18, 2016
Gaydukov R., Сибирские электронные математические известия 2024 Т. 21 № 1 С. 178-187
In this paper we study a Rayleigh-type equation on a semi-infinite cylinder with a Coulomb-type potential.
This equation arises in the double-deck boundary layer structure in the problem of flow induced by a uniformly rotating disk with small periodic irregularities on its surface for large Reynolds numbers. Using combined numerical and analytical approach, the existence of ...
Added: February 17, 2024
Danilov V. G., Gaydukov R. K., Russian Journal of Mathematical Physics 2017 Vol. 24 No. 1 P. 1-18
The problem of flow of a viscous incompressible fluid in an axially symmetric pipe with small irregularities on the wall is considered. An asymptotic solution of the problem with the double-deck structure of the boundary layer and the unperturbed flow in the environment (the “core flow”) is obtained. The results of flow numerical simulation in ...
Added: September 28, 2016
Gaydukov R. K., Fonareva A. V., Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 334-343
The problem of viscous compressible fluid flow in an axially symmetric pipe with small periodic irregularities on the wall is considered for large Reynolds numbers. An asymptotic solution with double-deck structure of the boundary layer and unperturbed core flow is obtained. Numerical investigations of the influence of the density of the core flow on the flow behavior in ...
Added: September 2, 2019
V. G. Danilov, R. K. Gaydukov, Russian Journal of Mathematical Physics 2022 Vol. 29 No. 4 P. 431-455
A problem of a nonstationary incompressible viscous fluid ow along a plate with small fast-oscillating irregularities on the surface for a large Reynolds number is considered by using rigorous methods of mathematical physics. Depending on the scales of irregularities in the problem under study, there arises a solution that describes the double-deck or triple-deck structure boundary layers on ...
Added: August 19, 2020
Gaidukov R.K., Danilov V.G., , in : Abstracts: Russian-French Workshop “Mathematical Hydrodynamics”, August 22–27, 2016. : Novosibirsk : [б.и.], 2016. P. 20-22.
We consider a non-stationary problem of an incompressible viscous fluid flow along surfaces with small irregularities for large Reynolds number, which have a formal asymptotic solution with a double-deck structure of the boundary layer. ...
Added: September 28, 2016
Gaydukov R., European Journal of Mechanics - B/Fluids 2018 Vol. 71 P. 59-65
We consider the problem of flow of a viscous compressible subsonic fluid along a flat plate with small localized (hump-type) irregularities on the surface for large Reynolds numbers. We obtain a formal asymptotic solution with double-deck structure of the boundary layer. We present the results of numerical simulation of the flow in the thin boundary ...
Added: November 20, 2017
Springer, 2013
Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry. ...
Added: February 20, 2013
Gorshkov O., Колпаков И. Ю., Афанасенко К. А., Академия педагогических идей «Новация» 2017 № 11 С. 146-153
Conditions of solvability of the Cauchy problem for one differential equation of the first order which hasn't been resolved by rather derivative are found in work. Conditions of solvability of the Cauchy problem were received with application theorem of the Leray–Schauder's type. ...
Added: October 15, 2020
А. Л. Бекларян, Математические заметки 2014 Т. 96 № 2 С. 310-313
In this paper we consider the first boundary-value problem for elliptic systems of high order, defined on unbounded domains, which solutions satisfy a condition of finiteness of the Dirichlet integral, also known as the energy integral ...
Added: August 8, 2014
Gordin V. A., М. : Физматлит, 2013
Описаны аналитические и численные методы исследования уравнений и систем в частных производных: гиперболических, параболических, эллиптических и смешанного типа, линейных и нелинейных. Список этих методов и приемов велик, и они должны дополнять друг друга: интегральные преобразования, вариационное исчисление, специальные функции, асимптотические методы, сплайны, рациональные аппроксимации.
Книга адресована читателю, который использует и аналитические, и численные, компьютерные ...
Added: March 18, 2013
Колпаков И. Ю., Современные проблемы науки и образования 2014 № 3
Conditions of solvability of a periodic boundary value problem for one differential equation of the first order which hasn't been resolved by rather derivative are found in work. Creation of mathematical models of some real processes leads to problems for the ordinary differential equations which haven't been resolved by rather senior derivative and, in particular, ...
Added: April 7, 2015
Gaydukov R., Сибирский журнал вычислительной математики 2022 Т. 15 № 2 С. 97-109
A viscous liquid flow along a semi-infinite plate with small periodic irregularities on the surface was
considered for large Reynolds numbers. The flow near the plate is described by Prandtl equations with
induced pressure which are non-classical PDE, because they contain a limiting term. The main goal is to
construct a numerical algorithm for solving these equations with ...
Added: June 10, 2020
Fonareva A. V., Gaydukov R. K., Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 224-243
A subsonic flow of a viscous compressible fluid in a two-dimensional channel with small periodic or localized irregularities on the walls for large Reynolds numbers is considered. A formal asymptotic solution with double-deck structure of the boundary layer is constructed. A nontrivial time hierarchy is discovered in the decks. An analysis of the scales of irregularities at ...
Added: March 22, 2021
Gaydukov R., European Journal of Mechanics - B/Fluids 2021 Vol. 89 P. 401-410
An asymptotic solution with double-deck boundary layer structure is constructed for the problem of an incompressible fluid flow along a semi-infinite plate with small localized or periodic (fast-oscillating) irregularities on the surface whose shape depends on time. Numerical simulation of flow in the near-plate region is presented for two types of the shape change: oscillations of the ...
Added: January 4, 2021
Тамбов : ТРОО "Бизнес-Наука-Общество", 2012
В сборнике научных трудов рассматривается современные вопросы науки и практики применения научных результатов по материалам международной заочной научно-практической конференции "Актуальные проблемы науки и образования:прошлое, настоящее, будущее" (29 марта 2012 г.) ...
Added: April 7, 2015
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020