Layered Three-Dimensional Nonuniform Viscous Incompressible Flows

Prosviryakov, E. Yu.; Спевак, Л. Ф.

doi:10.1134/s0040579518050391

Cited by 12 publications

(4 citation statements)

References 12 publications

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“…Физически это означает, что фактически жидкость заключена между двумя бесконечно протяженными плоскими недеформируемыми пластинами. Сразу оговоримся, что для задания давления на свободной границе zh  , строго говоря, используется приближение твердой крышки с заданием нулевых скоростей [8,14]. В этом случае тождественно выполняется кинематическое и динамическое граничное условие, а давление жидкости задано на свободной границе следующим образом:…”

Section: постановка краевой задачиunclassified

The Couette-Poiseuille Inhomogeneous Shear Flow at the Motion of the Lower Boundary of the Horizontal Layer

Goruleva¹,

Prosviryakov²

2021

HFIM

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Аннотация. В статье получено точное решение уравнений Навье-Стокса и уравнения несжимаемости. Это решение описывает установившееся изобарическое и градиентное неоднородное сдвиговое течение вязкой несжимаемой жидкости. Движение жидкости при постоянном давлении индуцируется движением нижней границы бесконечного горизонтального слоя жидкости. Неоднородное течение жидкости типа Пуазейля рассматривается при совместном задании постоянного горизонтального градиента давления и скоростей. Сдвиговое изотермическое течение вязкой несжимаемой жидкости описывается переопределенной системой уравнений в частных производных. Точное интегрирование уравнений Навье-Стокса осуществляется в классе Линя-Сидорова-Аристова. Поле скоростей и поле давления являются линейными формами относительно двух координат (горизонтальных или продольных координат). Коэффициенты линейных формы зависят от третьей (вертикальной или поперечной) координаты. Благодаря структуре точного решения, уравнение несжимаемости автоматически удовлетворяется. Таким образом, роль "лишнего" уравнения играет уравнение несжимаемости. Проведен анализ полученного полиномиального точного решения уравнений Навье-Стокса для несжимаемой жидкости. Неоднородное течение типа Куэтта характеризуется полиномом четвертой степени. Для описания модифицированного течения Пуазейля используется полином пятой степени. Исследование локализации корней полинома показало существование немонотонного профиля удельной кинетической энергии с двумя нулевыми значениями. Иными словами, в жидкости регистрируются противотечения.

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Section: постановка краевой задачиunclassified

The Couette-Poiseuille Inhomogeneous Shear Flow at the Motion of the Lower Boundary of the Horizontal Layer

Goruleva¹,

Prosviryakov²

2021

HFIM

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“…This result was a starting point for finding exact solutions that describe inhomogeneous shear flows. The first exact solution describing the inhomogeneous isobaric flow of Couette type for different boundary conditions was first announced in [54][55][56][57]. It was shown that taking into account the inhomogeneity of the velocity field entails the presence of a vertical swirl of fluid outside the Coriolis field.…”

Section: Introductionmentioning

confidence: 99%

“…In [54][55][56][57][58][59][60], use was made of an inhomogeneous velocity field which satisfies exactly the Navier -Stokes equations, to solve the problem of convection of a vertical vortex flow. Using an exact solution for the velocity field [54][55][56][57][58][59][60], an inhomogeneous Couette flow was considered in [61] in specifying the temperature gradients on the upper boundary. It was shown that the motion of the boundary leads to intensification of heat conduction from the heated boundary.…”

Section: Introductionmentioning

confidence: 99%

An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

Berestova¹,

Prosviryakov²

2023

Nelin. Dinam.

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An exact solution of the Oberbeck – Boussinesq equations for the description of the steady-state Bénard – Rayleigh convection in an infinitely extensive horizontal layer is presented. This exact solution describes the large-scale motion of a vertical vortex flow outside the field of the Coriolis force. The large-scale fluid flow is considered in the approximation of a thin layer with nondeformable (flat) boundaries. This assumption allows us to describe the large-scale fluid motion as shear motion. Two velocity vector components, called horizontal components, are taken into account. Consequently, the third component of the velocity vector (the vertical velocity) is zero. The shear flow of the vertical vortex flow is described by linear forms from the horizontal coordinates for velocity, temperature and pressure fields. The topology of the steady flow of a viscous incompressible fluid is defined by coefficients of linear forms which have a dependence on the vertical (transverse) coordinate. The functions unknown in advance are exactly defined from the system of ordinary differential equations of order fifteen. The coefficients of the forms are polynomials. The spectral properties of the polynomials in the domain of definition of the solution are investigated. The analysis of distribution of the zeroes of hydrodynamical fields has allowed a definition of the stratification of the physical fields. The paper presents a detailed study of the existence of steady reverse flows in the convective fluid flow of Bénard – Rayleigh – Couette type.

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“…In other words, the family of velocities (4) can describe vertical spin in a fluid, which occurs without setting rotation at the boundaries of the region in question. The class of exact solutions (4) for the Oberbeck-Boussinesq equation system allows large-scale flows in the equatorial zone of the World Ocean to be studied with the use of the traditional approximation for the angular velocity vector (one Coriolis parameter is used) [38,44,55,56,59,60].…”

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confidence: 99%

Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation

Burmasheva

Prosviryakov

2019

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

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This article discusses the solvability of an overdetermined system of heat convection equations in the Boussinesq approximation. The Oberbeck-Boussinesq system of equations, supplemented by an incompressibility equation, is overdetermined. The number of equations exceeds the number of unknown functions, since non-uniform layered flows of a viscous incompressible fluid are studied (one of the components of the velocity vector is identically zero). The solvability of the non-linear system of Oberbeck-Boussinesq equations is investigated. The solvability of the overdetermined system of non-linear Oberbeck-Boussinesq equations in partial derivatives is studied by constructing several particular exact solutions. A new class of exact solutions for describing three-dimensional non-linear layered flows of a vertical swirling viscous incompressible fluid is presented. The vertical component of vorticity in a non-rotating fluid is generated by a non-uniform velocity field at the lower boundary of an infinite horizontal fluid layer. Convection in a viscous incompressible fluid is induced by linear heat sources. The main attention is paid to the study of the properties of the flow velocity field. The dependence of the structure of this field on the magnitude of vertical twist Research Article c b The content is published under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/) Please cite this article in press as: B u r m a s h e v a N. V., P r o s v i r y a k o v E. Yu. Convective layered flows of a vertically whirling viscous incompressible fluid. B u r m a s h e v a N. V., P r o s v i r y a k o v E. Yu.is investigated. It is shown that, with nonzero vertical twist, one of the components of the velocity vector allows stratification into five zones through the thickness of the layer under study (four stagnant points). The analysis of the velocity field has shown that the kinetic energy of the fluid can twice take the zero value through the layer thickness.

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Layered Three-Dimensional Nonuniform Viscous Incompressible Flows

Cited by 12 publications

References 12 publications

The Couette-Poiseuille Inhomogeneous Shear Flow at the Motion of the Lower Boundary of the Horizontal Layer

The Couette-Poiseuille Inhomogeneous Shear Flow at the Motion of the Lower Boundary of the Horizontal Layer

An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation

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