On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equations
In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations. But there is an essential deficiency of non-stationary solutions indeed.In our presentation, we proceed exploring the case of non-stationary helical flows of the N...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2020-01-01
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| Series: | Journal of King Saud University: Science |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364718306335 |
| _version_ | 1811273132634275840 |
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| author | Sergey V. Ershkov Roman V. Shamin Ayrat R. Giniyatullin |
| author_facet | Sergey V. Ershkov Roman V. Shamin Ayrat R. Giniyatullin |
| author_sort | Sergey V. Ershkov |
| collection | DOAJ |
| description | In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations. But there is an essential deficiency of non-stationary solutions indeed.In our presentation, we proceed exploring the case of non-stationary helical flows of the Navier-Stokes equations for incompressible fluids, with variable (spatially dependent) coefficient of proportionality α between velocity and the curl field of flow.The main motivation of the current research is the exploring the case when velocity field u is supposed to be perpendicular to the vector ∇α. Conditions for the existence of the exact solution for the aforementioned type of flows are obtained, for which non-stationary helical flow with invariant Bernoulli-function is considered.The spatial part of the pressure field of the fluid flow should be determined via Bernoulli-function, if components of the velocity of the flow are already obtained. Keywords: Navier-Stokes equations, Non-stationary helical flow, Arnold-Beltrami-Childress (ABC) flow |
| first_indexed | 2024-04-12T22:53:48Z |
| format | Article |
| id | doaj.art-9c6f6c2ce04b4381b4a204afd3d7f161 |
| institution | Directory Open Access Journal |
| issn | 1018-3647 |
| language | English |
| last_indexed | 2024-04-12T22:53:48Z |
| publishDate | 2020-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of King Saud University: Science |
| spelling | doaj.art-9c6f6c2ce04b4381b4a204afd3d7f1612022-12-22T03:13:16ZengElsevierJournal of King Saud University: Science1018-36472020-01-01321459467On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equationsSergey V. Ershkov0Roman V. Shamin1Ayrat R. Giniyatullin2Nizhny Novgorod State Technical University n.a. R.E. Alekseev, 24 Minina st., Nizhny Novgorod 603155, Russia; Corresponding author.Moscow Technological University (MIREA), 78 Vernadsky Avenue, Moscow 119454, RussiaNizhny Novgorod State Technical University n.a. R.E. Alekseev, 24 Minina st., Nizhny Novgorod 603155, RussiaIn fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations. But there is an essential deficiency of non-stationary solutions indeed.In our presentation, we proceed exploring the case of non-stationary helical flows of the Navier-Stokes equations for incompressible fluids, with variable (spatially dependent) coefficient of proportionality α between velocity and the curl field of flow.The main motivation of the current research is the exploring the case when velocity field u is supposed to be perpendicular to the vector ∇α. Conditions for the existence of the exact solution for the aforementioned type of flows are obtained, for which non-stationary helical flow with invariant Bernoulli-function is considered.The spatial part of the pressure field of the fluid flow should be determined via Bernoulli-function, if components of the velocity of the flow are already obtained. Keywords: Navier-Stokes equations, Non-stationary helical flow, Arnold-Beltrami-Childress (ABC) flowhttp://www.sciencedirect.com/science/article/pii/S1018364718306335 |
| spellingShingle | Sergey V. Ershkov Roman V. Shamin Ayrat R. Giniyatullin On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equations Journal of King Saud University: Science |
| title | On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equations |
| title_full | On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equations |
| title_fullStr | On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equations |
| title_full_unstemmed | On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equations |
| title_short | On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equations |
| title_sort | on a new type of non stationary helical flows for incompressible 3d navier stokes equations |
| url | http://www.sciencedirect.com/science/article/pii/S1018364718306335 |
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