Double-deck structure in the fluid flow problem over plate with small irregularities of time-dependent shape
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 amplitude of irregularities and motion of the irregularity in the upstream and downstream directions. The influence of the time-dependent shape on the flow behavior (including the vortex formation process) is shown in detail.
Research target: Mathematics
Priority areas: mathematics
, , 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
Double-deck structure in the power-law non-Newtonian fluid flow along a plate with small localized irregularities
, 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
Nonstationary double-deck structure of boundary layers in compressible flow problem inside a channel with small irregularities on the walls
, , 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
Double-deck structure in the fluid flow induced by a uniformly rotating disk with small symmetric irregularities on its surface
, , 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
, , Mathematische Nachrichten 2020 Vol. 293 P. 210-225
We consider fourth order ordinary differential operators on the half-line and on the line, where the perturbation has compactly supported coefficients. The Fredholm determinant for this operator is an analytic function in the whole complex plane without zero.We describe the determinant at zero.We show that in the generic case it has a pole of order 4 in the case ...
Added: February 5, 2021
, , , Russian Journal of Mathematical Physics 2020 Vol. 27 No. 4 P. 456-468
We find the logarithmic asymptotics as T tends to infinity of the number of partitions of positive numbers not exceeded T into sums of positive numbers t_j with j less or equal k, where the counting function of t_j grows as a power of j. The asymptotics is uniform with respect to k. ...
Added: October 31, 2020
, , 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
, Математические заметки 2017 Т. 102 № 6 С. 816-827
Asymptotic formulas are obtained for a class of integrals that are Fourier transforms of rapidly oscillating functions. These formulas contain special functions and generalize the well-known method of stationary phase. ...
Added: January 13, 2018
, , , International Journal for Computational Civil and Structural Engineering 2018 Vol. 14 No. 1 P. 92-101
The filtration problem in a porous medium is an important part of underground hydromechanics. Filtration of suspensions and colloids determines the processes of strengthening the soil and creating waterproof walls in the ground while building the foundations of buildings and underground structures. It is assumed that the formation of a deposit is dominated by the ...
Added: July 1, 2018
, , Вестник Московского государственного строительного университета 2017 No. 11 P. 1278-1283
Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck ...
Added: January 6, 2018
, , Russian Journal of Mathematical Physics 2023
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
Double-deck structure of the boundary layer in the problem of flow in an axially symmetric pipe with small irregularities on the wall for large Reynolds numbers
, , 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
Численное исследование локализованного возмущения температуры в модели фазового поля в случае слияния свободных границ
, , Журнал вычислительной математики и математической физики 2012 Т. 52 № 11 С. 2080-2092
Исследуется эффект локализованного в пространстве и времени возмущения температуры, которое возникает в точке контакта свободных границ в задаче Стефана–Гиббса–Томсона в рамках модели фазового поля. ...
Added: December 24, 2012
Asymptotic multiscale solutions to Navier–Stokes equations with fast oscillating perturbations in boundary layers
, , 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
On the asymptotics of the element counting function in an additive arithmetic semigroup with exponential counting function of prime generators
, , , Functional Analysis and Its Applications 2016 Vol. 50 No. 4 P. 291-307
We find the asymptotics of the element counting function for an additive arithmetic semigroup with exponential growth of the counting function of prime generators. ...
Added: October 18, 2015
АЛГОРИТМ ЧИСЛЕННОГО РЕШЕНИЯ СИСТЕМЫ УРАВНЕНИЙ ПРАНДТЛЯ С ИНДУЦИРОВАННЫМ ДАВЛЕНИЕМ В ПЕРИОДИЧЕСКОМ СЛУЧАЕ
, 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
Double-Deck Structure of the Boundary Layer in Problems of Flow around Localized Perturbations on a Plate
, , 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
, , et al., Труды НГТУ им. Р.Е. Алексеева 2012 № 2(95) С. 48-65
Purpose: Numerical modeling of internal baroclinic disturbances of different shapes in a model lake with variable depth, analysis of velocity field of wave-induced current, especially in the near-bed layer. Approach: The study is carried out with the use of numerical full nonlinear nonhydrostatic model for stratified fluid. Findings: The full nonlinear numerical modeling of internal wave dynamics ...
Added: October 6, 2012
, , Вестник Московского государственного строительного университета 2014 № 7 С. 34-40
A classic pursuit problem is studied in which two material points - a Pursuer and a Pursued - move in a plane at constant speeds. The velocity vector of the Pursued does not change its direction and the velocity vector of the Pursuer turns and always aims at the Pursued. If the Pursuer moves at ...
Added: August 3, 2014
, , 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
, , 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
Асимптотики решений задач обтекания несжимаемой жидкостью поверхностей c малыми неровностями при больших числах Рейнольдса
, , 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
, Mathematics of Computation 2017 Vol. 86 No. 305 P. 1499-1524
For an arbitrary set of nonnegative integers, we consider the Euler binary partition function which equals the total number of binary expansions of an integer with ``digits'' from . By applying the theory of subdivision schemes and refinement equations, the asymptotic behaviour of as is characterized. For all finite , we compute the lower and upper exponents of growth of , find when ...
Added: May 11, 2017
Асимптотическое поведение собственных значений оператора Шредингера в тонких бесконечных и тонких замкнутых трубках
, Наноструктуры. Математическая физика и моделирование 2012 Т. 7 № 2 С. 17-44
В работе получено асимптотическое разложение собственных значений оператора Лапласа с нулевыми данными Дирихле в бесконечных трубках, т. е. в бесконечных изогнутых цилиндрах с внутренним кручением при равномерном сжатии поперечных сечений, по малому параметру, характеризующему поперечные размеры трубки. Аналогичное разложение получено для оператора Шредингера с учетом магнитного поля для конечных изогнутых трубок. Предложен метод сведения задачи ...
Added: December 24, 2012