The Couette problem for a Kelvin–Voigt medium

Пухначев, В. В.; Pukhnacheva, T. P.

doi:10.1007/s10958-012-1003-0

Cited by 4 publications

(3 citation statements)

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“…Note that there exists the well-known exact Taylor-Couette solution on the fluid flow in the gap between coaxial cylinders [2,[4][5][6][7][8], as well as the solution describing isobaric fluid flow on a sphere [9,10]. The Couette flow is fundamental in the study of fluids with non-Newtonian properties [11,12]. The three-dimensional Couette flow, which is potential and non-isobaric, has been recently exemplified [13].…”

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“…It is of interest that, despite seemingly simple structure of boundary conditions (11), (12) and velocity field representation (11), (12), the obtained solution ( 15)-( 20) depends on the parameters of the boundary problem under study and the physical characteristics of the fluid in an extremely non-trivial way. Therefore, in a general form, it is impossible to make any conclusions about the effect of a specific parameter on the structure of the final solution.…”

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Inhomogeneous Couette flows for a two-layer fluid

Burmasheva,

Larina,

Prosviryakov

2023

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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Предложено новое точное решение уравнений Навье-Стокса, описывающее установившееся изобарическое изотермическое течение стратифицированной по плотности и/или вязкости несжимаемой двуслойной жидкости. Указанное точное решение принадлежит классу функций, линейных по части пространственных координат, и является обобщением классического течения Куэтта в протяженном горизонтальном слое на случай неодномерных неоднородных течений. В качестве системы краевых условий рассмотрена связка «условие прилипания + воздействие параболического ветра». На общей границе двух слоев заявлено выполнение требования гладкости и непрерывности решения. Построенное для каждого слоя решение было исследовано на предмет возможности описывать возникновение застойных точек поля скорости и генерации противотечений. Строго показано, что указанное решение при определенном граничном управлении и варьировании геометрико-физических характеристик слоя отвечает множественной стратификации как поля скорости, так и порождаемого им поля касательных напряжений.

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confidence: 99%

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confidence: 99%

Inhomogeneous Couette flows for a two-layer fluid

Burmasheva,

Larina,

Prosviryakov

2023

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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“…С теоретической точки зрения решение Куэтта востребовано в теории гидродинамической устойчивости [21][22][23][24][25][26][27][28][29][30][31][32][33]. Известно, что использование профиля Куэтта в качестве основного течения используется при изучении влияния различных типов возмущений (вторичных течений) на структуру изотермических гидродинамических потоков в бесконечно протяженных слоях жидкости, в областях с цилиндрической и сферической симметрией [21][22][23][24][25][26][27][28][29][30][31][32][33].…”

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Exact solutions of the Navier–Stokes equations for describing an isobaric one-directional vertical vortex flow of a fluid

Burmasheva¹,

Prosviryakov²

2021

DREAM

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The article proposes a family of exact solutions to the Navier–Stokes equations for describing isobaric inhomogeneous unidirectional fluid motions. Due to the incompressibility equation, the velocity of the inhomogeneous Couette flow depends on two coordinates and time. The expression for the velocity field has a wide functional arbitrariness. This exact solution is obtained by the method of separation of variables, and both algebraic operations (additivity and multiplicativity) are used to substantiate the importance of modifying the classical Couette flow. The article contains extensive bibliographic information that makes it possible to trace a change in the exact Couette solution for various areas of the hydrodynamics of a Newtonian incompressible fluid. The fluid flow is described by a polynomial depending on one variable (horizontal coordinate). The coefficients of the polynomial functionally depend on the second (vertical) coordinate and time; they are determined by a chain of the simplest homogeneous and inhomogeneous partial differential parabolic-type equations. The chain of equations is obtained by the method of undetermined coefficients after substituting the exact solution into the Navier–Stokes equation. An algorithm for integrating a system of ordinary differential equations for studying the steady motion of a viscous fluid is presented. In this case, all the functions defining velocity are polynomials. It is shown that the topology of the vorticity vector and shear stresses has a complex structure even without convective mixing (creeping flow).

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Layered Three-Dimensional Nonuniform Viscous Incompressible Flows

Prosviryakov

Спевак

2018

Theor Found Chem Eng

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The Couette problem for a Kelvin–Voigt medium

Cited by 4 publications

References 4 publications

Inhomogeneous Couette flows for a two-layer fluid

Inhomogeneous Couette flows for a two-layer fluid

Exact solutions of the Navier–Stokes equations for describing an isobaric one-directional vertical vortex flow of a fluid

Layered Three-Dimensional Nonuniform Viscous Incompressible Flows

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