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## Equations for velocity oscillations in problems of a fluid flow along a plate with small periodic irregularities on the surface for large Reynolds numbers

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.

Keywords: Double-deck structureRayleigh-type equationperiodic irregularitiesTriple-deck strucutreBenjamin-Ono equation

Publication based on the results of:

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

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 ...

Added: September 3, 2015

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

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., Fonareva A. V., European Journal of Mechanics - B/Fluids 2022 Vol. 94 P. 50-59

The problem of a rotating disk with slightly perturbed surface immersed in a viscous fluid is considered.
The asymptotic solutions with double-deck structure of the boundary layer are constructed for symmetric
periodic and localized types of irregularities on the disk surface for large Reynolds numbers. The paper
presents the results of numerical simulations of the flow near the ...

Added: November 14, 2021

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., 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

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

Danilov V., Gaydukov R., Russian Journal of Mathematical Physics 2023 Vol. 30 No. 2 P. 165-175

In this paper, we construct and study a model of a phase transition in a system of two
phases (liquid and ice) and three media — water, a piece of ice, and some nonmeltable
solid substrate. Namely, the melting-crystallization process is considered in the problem
of water flow along a small ice irregularity (such as a frozen drop) ...

Added: December 14, 2022

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

Flamarion M. V., Pelinovsky E., Symmetry 2023 Vol. 15 No. 8 Article 1478

This study aims to explore the complex interactions between an internal solitary wave and
an external force using the Benjamin-Ono equation as the theoretical framework. The investigation
encompasses both asymptotic and numerical approaches. By assuming a small amplitude for the
external force, we derive a dynamical system that describes the behavior of the solitary wave
amplitude and the position ...

Added: July 26, 2023

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., Journal of Non-Newtonian Fluid Mechanics 2021

The asymptotic solution with double-deck structure was obtained in the problem of flow
of a non-Newtonian fluid with power-law rheological properties along a semi-infinite plate
with a small localized irregularity on the surface for large Reynolds numbers. The numerical
modeling of the flow in the region near the surface was performed for different fluid indexes.
The results of investigations ...

Added: November 14, 2021

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

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., , in : Proceedings of the International Conference DAYS on DIFFRACTION 2019. : IEEE, 2019. P. 51-56.

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. ...

Added: November 1, 2019

Gaydukov R.K., Burov N.A., Acta Applicandae Mathematicae 2023

We investigate 3D problem of an incompressible fluid flow along a plate with smal localized irregularities for large Reynolds number. The formal asymptotic solution with double-deck boundary layer structure is constructed. The resuls of numerical simulation of fluid flow near surfaces is presented. ...

Added: June 10, 2023