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## Double-deck structure of the boundary layer in the problem of a compressible flow along a plate with small irregularities on the surface

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 the near-boundary region).

Keywords: численное моделированиеDouble-deck structureдвухпалубная структуратеория пограничного слояnumerical simulationsboundary layer theoryperiodic irregularitiesformal asymptoticscompressible fluid mechanicsпериодические возмущенияформальные асимптотикисжимаемые течения

Publication based on the results of:

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

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

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 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., 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

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

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., 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., Сибирские электронные математические известия 2024 Т. 21 № 1 С. 177-186

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

Gromov E.M., Malomed B. A., Physica Scripta 2015 Vol. 90 No. 6 P. 068021-1-068021-6

Dynamics of Langmuir solitons is considered in plasmas with spatially inhomogeneous electron temperature. An underlying Zakharov-type system of two unidirectional equations for the Langmuir and ion-sound fields is reduced to an inhomogeneous nonlinear Schrödinger equation (NLSE) with spatial variation of the second-order dispersion (SOD) and self-phase modulation (SPM) coefficients, induced by the spatially inhomogeneous profile ...

Added: April 25, 2015

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., Журнал вычислительной математики и математической физики 2024 № 6

Работа посвящена математическому моделированию фазового перехода лед–вода при течение жидкости внутри трубы с малым ледяным наростом на стенке при больших числах Рейнольдса. В качестве математической модели, описывающей динамику фазового перехода, используется двухпалубная модель пограничного слоя и система фазового поля. Приведены результаты численного моделирования. ...

Added: February 17, 2024

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

Талипова Т. Г., Kurkina O. E., Терлецкая Е. В. et al., Экологические системы и приборы 2014 № 3 С. 26-38

Necessity of study of the internal waves of large amplitude in the Barents Sea related to their possible catastrophic effects on
offshore platforms, powerful transport sediments and bottom erosion, which invariably affects on the overall environmental
situation. In this paper, numerical simulation of the generation and propagation of internal waves in the Barents Sea in
the framework of ...

Added: May 13, 2014

Купцов П. В., Stankevich N., Известия высших учебных заведений. Прикладная нелинейная динамика 2024 Т. 32 № 1 С. 72-95

Цель настоящего исследования — представить подробное описание процедуры создания и обучения нейросетевого отображения на примере моделирования динамики нейронного осциллятора типа Ходжкина–Хаксли; показать, что нейросетевые отображения, обученные для одиночного осциллятора, можно использовать в качестве элементов связанной системы, моделирующей поведение связанных осцилляторов. Методы. В работе используется численный метод решения жёстких систем обыкновенных дифференциальных уравнений. Также применяется процедура ...

Added: December 13, 2023

Aseeva N., Gromov E., Tyutin V. V., Radiophysics and Quantum Electronics 2013 Vol. 56 No. 3 P. 157-166

We consider the soliton dynamics in terms of the extended nonlinear Schr¨odinger equation taking into account the inhomogeneous linear second-order dispersion (SOD) and stimulated scattering by damped low-frequency waves (SSDW). It is shown that the wave number downshift due to SSDW is compensated by an upshift due to the SOD decrease on the spatial coordinate. ...

Added: October 8, 2013

Gromov E.M., Malomed B. A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2015 Vol. 92 No. 6 P. 062926-1-062926-7

Dynamics of solitons is considered in the framework of an extended nonlinear Schrödinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped low-frequency (LF) internal waves. The drive gives rise to a convective (but not absolute) instability in the system. The resulting NLSE ...

Added: December 5, 2015

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

Marshirov V. V., Marshirova L. E., Литейное производство 2017 № 9 С. 29-33

The presented mathematical model is based on the use of the finite difference method. The model is implemented as a web application and allows users to explore the features of the solidification process and calculate the frequency of impulse actions. Using the model, the required frequencies for casting with a thickness of 7 mm were ...

Added: November 13, 2017

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

Mikheev A. V., Теория. Практика. Инновации 2017 № 9 (21)

In this paper we consider the calculation of a dynamical system described by a second-order differential equation in which a fundamental system of solutions consisting of functions of exponential type is replaced by bounded functions of the Verhulst model. The time dependence of the forces acting on the dynamical system is analyzed, and the obtained ...

Added: September 6, 2017

Gaydukov R., Russian Journal of Nonlinear Dynamics 2024 Vol. 20 No. 1 P. 1-13

The problem of flow of a non-Newtonian viscous fluid with power-law rheological properties
along a semi-infinite plate with a small localized irregularity on the surface is considered for large
Reynolds numbers. The asymptotic solution with double-deck structure of the boundary layer is
constructed. The numerical simulation of the flow in the region near the surface was performed
for different ...

Added: December 26, 2023

Marshirov V. V., Marshirova L. E., Литейное производство 2015 № 9 С. 31-34

The article describes the information environment that allows users to simulate the process of solidification. In this environment, the user can calculate the formation of temperature fields and moving the fronts of phases. The results can be presented in tables and graphs. The information environment is accessible and open to change. Possibilities of practical use ...

Added: December 24, 2015