Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на этот ресурс: http://elar.urfu.ru/handle/10995/89961
Название: Nonlinear gradient flow of a vertical vortex fluid in a thin layer
Авторы: Privalova, V. V.
Prosviryakov, E. Yu.
Simonov, M. A.
Дата публикации: 2019
Издатель: Institute of Computer Science Izhevsk
Библиографическое описание: Privalova, V. V. Nonlinear gradient flow of a vertical vortex fluid in a thin layer / V. V. Privalova, E. Yu. Prosviryakov, M. A. Simonov. — DOI 10.20537/nd190306 // Russian Journal of Nonlinear Dynamics. — 2019. — Vol. 3. — Iss. 15. — P. 271-283.
Аннотация: A new exact solution to the Navier – Stokes equations is obtained. This solution describes the inhomogeneous isothermal Poiseuille flow of a viscous incompressible fluid in a horizontal infinite layer. In this exact solution of the Navier – Stokes equations, the velocity and pressure fields are the linear forms of two horizontal (longitudinal) coordinates with coefficients depending on the third (transverse) coordinate. The proposed exact solution is two-dimensional in terms of velocity and coordinates. It is shown that, by rotation transformation, it can be reduced to a solution describing a three-dimensional flow in terms of coordinates and a two-dimensional flow in terms of velocities. The general solution for homogeneous velocity components is polynomials of the second and fifth degrees. Spatial acceleration is a linear function. To solve the boundary-value problem, the no-slip condition is specified on the lower solid boundary of the horizontal fluid layer, tangential stresses and constant horizontal (longitudinal) pressure gradients specified on the upper free boundary. It is demonstrated that, for a particular exact solution, up to three points can exist in the fluid layer at which the longitudinal velocity components change direction. It indicates the existence of counterflow zones. The conditions for the existence of the zero points of the velocity components both inside the fluid layer and on its surface under nonzero tangential stresses are written. The results are illustrated by the corresponding figures of the velocity component profiles and streamlines for different numbers of stagnation points. The possibility of the existence of zero points of the specific kinetic energy function is shown. The vorticity vector and tangential stresses arising during the flow of a viscous incompressible fluid layer under given boundary conditions are analyzed. It is shown that the horizontal components of the vorticity vector in the fluid layer can change their sign up to three times. Besides, tangential stresses may change from tensile to compressive, and vice versa. Thus, the above exact solution of the Navier – Stokes equations forms a new mechanism of momentum transfer in a fluid and illustrates the occurrence of vorticity in the horizontal and vertical directions in a nonrotating fluid. The three-component twist vector is induced by an inhomogeneous velocity field at the boundaries of the fluid layer. © 2019 Institute of Computer Science Izhevsk. All rights reserved.
Ключевые слова: COUNTERFLOW
EXACT SOLUTION
GRADIENT FLOW
POISEUILLE FLOW
STAGNATION POINT
VORTICITY
URI: http://elar.urfu.ru/handle/10995/89961
Условия доступа: info:eu-repo/semantics/openAccess
cc-by-nd
Идентификатор РИНЦ: 42534793
Идентификатор SCOPUS: 85088502943
Идентификатор PURE: 13898951
ISSN: 2658-5324
DOI: 10.20537/nd190306
Сведения о поддержке: 19-19-00571
The work was supported by the Russian Scientific Foundation (project 19-19-00571).
Карточка проекта РНФ: 19-19-00571
Располагается в коллекциях:Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC

Файлы этого ресурса:
Файл Описание РазмерФормат 
10.20537-nd190306.pdf387,31 kBAdobe PDFПросмотреть/Открыть


Все ресурсы в архиве электронных ресурсов защищены авторским правом, все права сохранены.