On a new Lagrangian view on the evolution of vorticity in spatial flows
The purpose of the study is to extend to the spatial case proposed by G.B.Sizykh approach to a two-dimensional vorticity evolution, which is based on the idea of considering a vorticity evolution in the form of such a motion of vortex lines and tubes that the intensity of these tubes changes over ti...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2022-03-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/100273/pdf_1 |
| _version_ | 1811330408473690112 |
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| author | Ivan A. Maksimenko Vladimir V. Markov |
| author_facet | Ivan A. Maksimenko Vladimir V. Markov |
| author_sort | Ivan A. Maksimenko |
| collection | DOAJ |
| description | The purpose of the study is to extend to the spatial case proposed by G.B.Sizykh approach to a two-dimensional vorticity evolution, which is based on the idea of considering a vorticity evolution in the form of such a motion of vortex lines and tubes that the intensity of these tubes changes over time according to a predefined law.Method.Thorough analysis is determined by describing the flow velocity field of an ideal incompressible fluid and a viscous gas in the general case, using the idea of the movement of imaginary particles.Results.For any given time law of change of velocity circulation (i.e. for an exponential decay) of a real fluid along the contours the method of evaluating the field of velocity of such contours and vortex tubes is proposed (e.g. getting a field of imaginary particles, which transfer them). It is established that for a given time law the velocity of imaginary particles is determined ambiguously, and the method of how to adjust their motion preserving defined law of circulation change is proposed.Conclusion.A new Lagrangian approach to the evolution of vorticity in three-dimensional flows is derived, as well as the expressions for the contours' velocity, which imply stated changing over the time of the velocity circulation of a real fluid along any contour. This theoretical result can be utilized in spatial modifications of the viscous vortex domain method to limit the number of vector tubes used in calculations. |
| first_indexed | 2024-04-13T16:02:17Z |
| format | Article |
| id | doaj.art-96ea9c6992e946a0b6f7000c26c7c95c |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T16:02:17Z |
| publishDate | 2022-03-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-96ea9c6992e946a0b6f7000c26c7c95c2022-12-22T02:40:31ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812022-03-0126117918910.14498/vsgtu190777812On a new Lagrangian view on the evolution of vorticity in spatial flowsIvan A. Maksimenko0https://orcid.org/0000-0001-8159-8531Vladimir V. Markov1https://orcid.org/0000-0003-2188-2201Technical University of MunichSteklov Mathematical Institute, Russian Academy of SciencesThe purpose of the study is to extend to the spatial case proposed by G.B.Sizykh approach to a two-dimensional vorticity evolution, which is based on the idea of considering a vorticity evolution in the form of such a motion of vortex lines and tubes that the intensity of these tubes changes over time according to a predefined law.Method.Thorough analysis is determined by describing the flow velocity field of an ideal incompressible fluid and a viscous gas in the general case, using the idea of the movement of imaginary particles.Results.For any given time law of change of velocity circulation (i.e. for an exponential decay) of a real fluid along the contours the method of evaluating the field of velocity of such contours and vortex tubes is proposed (e.g. getting a field of imaginary particles, which transfer them). It is established that for a given time law the velocity of imaginary particles is determined ambiguously, and the method of how to adjust their motion preserving defined law of circulation change is proposed.Conclusion.A new Lagrangian approach to the evolution of vorticity in three-dimensional flows is derived, as well as the expressions for the contours' velocity, which imply stated changing over the time of the velocity circulation of a real fluid along any contour. This theoretical result can be utilized in spatial modifications of the viscous vortex domain method to limit the number of vector tubes used in calculations.https://journals.eco-vector.com/1991-8615/article/viewFile/100273/pdf_1contour velocityvelocity circulationspeed of imaginary particleszoravski's criterionfriedmann's theoremviscous vortex domain method |
| spellingShingle | Ivan A. Maksimenko Vladimir V. Markov On a new Lagrangian view on the evolution of vorticity in spatial flows Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki contour velocity velocity circulation speed of imaginary particles zoravski's criterion friedmann's theorem viscous vortex domain method |
| title | On a new Lagrangian view on the evolution of vorticity in spatial flows |
| title_full | On a new Lagrangian view on the evolution of vorticity in spatial flows |
| title_fullStr | On a new Lagrangian view on the evolution of vorticity in spatial flows |
| title_full_unstemmed | On a new Lagrangian view on the evolution of vorticity in spatial flows |
| title_short | On a new Lagrangian view on the evolution of vorticity in spatial flows |
| title_sort | on a new lagrangian view on the evolution of vorticity in spatial flows |
| topic | contour velocity velocity circulation speed of imaginary particles zoravski's criterion friedmann's theorem viscous vortex domain method |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/100273/pdf_1 |
| work_keys_str_mv | AT ivanamaksimenko onanewlagrangianviewontheevolutionofvorticityinspatialflows AT vladimirvmarkov onanewlagrangianviewontheevolutionofvorticityinspatialflows |