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12 August 2020
‘Scholars Are Humans, and You Shouldn’t Be Afraid of Them’
ICEF not only trains professionals in economics and finance, but also provides a perfect start for an academic career. Daniil Esaulov, lecturer, coordinator of student research work at ICEF and manager of ICEF Academia project, talked to us about how ICEF develops research skills, what students do at ICEF Academia, and why one shouldn’t be afraid of authorities in research.
11 August 2020
Coronavirus Was Brought into Russia at Least 67 Times
Many people in Russia believe that they had COVID-19 as early as December 2019 or January 2020. Is it possible to find out when the epidemic really started in Russia and where it came from? Bioinformatics provides an answer.
10 August 2020
Mathematics of Natural Choices: The Borda Count and Independence of Irrelevant Alternatives
Eric Maskin spoke at a recent research seminar held by the Centre in which he proposed a modified independence of irrelevant alternatives condition (IIA) and demonstrated that the voting rule satisfies modified IIA, Arrow’s other conditions, and May’s axioms if and only if it is the Borda count, i.e., rank-order voting. Fuad Aleskerov discussed how this affected the collective choice theory, elaborating on various choice models, starting from the Condorcet paradox.

Book chapter

Multideck structures of boundary layers in compressible flows

P. 51-56.
Gaydukov R., Danilov V.

Equations describing the double- and triple-deck structure are demonstrated for the case of compressible flows along a small perturbed plate for large Reynolds numbers. Numerical and analytical investigations of the influence of the upstream flow on the behavior of the flow in the near-wall region are presented.

Language: English
DOI
Keywords: Double-deck structureTriple-deck structureasymptoticcompressible flowboundary layer theory
Publication based on the results of: Mathematical Modeling of Resonance SystemsMathematical modeling of resonance systems(2019)

In book

Proceedings of the International Conference DAYS on DIFFRACTION 2019
IEEE, 2019.
Similar publications
Асимптотики решений задач обтекания несжимаемой жидкостью поверхностей c малыми неровностями при больших числах Рейнольдса
Гайдуков Р. К., Данилов В. Г. 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 a formal asymptotic solution of a problem of a flow inside an axially-symmetric pipe and a two-dimensional channel with small periodic irregularities on the wall. We prove that a quasistationary solution of a Rayleigh-type equation (which describes the flow oscillation on the “upper deck” of the boundary layer with the double-deck structure, i.e. in the classical Prandtl boundary layer) exists and is stable. We obtain a formal asymptotic solution with the double-deck structure for the problem of fluid flow along a plate with small localized irregularities such as hump, step or small angle. We construct a numerical solution algorithm for all equations which we obtained and we show the results of their applications.

Added: Sep 27, 2016
Double-deck structures of boundary layers in flows
Gaidukov R.K., Danilov V.G. In bk.: Abstracts: Russian-French Workshop “Mathematical Hydrodynamics”, August 22–27, 2016. Novosibirsk: 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: Sep 28, 2016
Vortices in the Prandtl boundary layer induced by irregularities on a plate
Danilov V., Gaydukov R. 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.

 

Added: Sep 3, 2015
Equations for velocity oscillations in problems of a fluid flow along a plate with small periodic irregularities on the surface for large Reynolds numbers
Gaydukov R., Danilov V. In bk.: Proceedings of the International Conference DAYS on DIFFRACTION 2018. IEEE, 2018. P. 118-123.

Depending on the scales of periodic irregularities in the problem under study, a solution arises which describes two (“double-deck”) or three (“triple-deck”) boundary layers on the plate. Mainly, we study the equations describing the velocity oscillations in the boundary layers arising because of periodic irregularities and show their command nature.

Added: Sep 18, 2018