Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4 †
The renormalization group approach and the operator product expansion technique are applied to the model of a passively advected vector field by a turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered in the vicini...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-01-01
|
| Series: | Universe |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2218-1997/5/1/37 |
| _version_ | 1798003812033626112 |
|---|---|
| author | Nikolay V. Antonov Nikolay M. Gulitskiy Maria M. Kostenko Tomáš Lučivjanský |
| author_facet | Nikolay V. Antonov Nikolay M. Gulitskiy Maria M. Kostenko Tomáš Lučivjanský |
| author_sort | Nikolay V. Antonov |
| collection | DOAJ |
| description | The renormalization group approach and the operator product expansion technique are applied to the model of a passively advected vector field by a turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered in the vicinity of space dimension d = 4 and the perturbation theory is constructed within a double expansion scheme in y and ε = 4 − d , where y describes scaling behaviour of the random force that enters the Navier-Stokes equation. The properties of the correlation functions are investigated, and anomalous scaling and multifractal behaviour are established. All calculations are performed in the leading order of y, ε expansion (one-loop approximation). |
| first_indexed | 2024-04-11T12:13:41Z |
| format | Article |
| id | doaj.art-31a1f7c3228447c7b5ed2048692781ed |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-04-11T12:13:41Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-31a1f7c3228447c7b5ed2048692781ed2022-12-22T04:24:28ZengMDPI AGUniverse2218-19972019-01-01513710.3390/universe5010037universe5010037Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4 †Nikolay V. Antonov0Nikolay M. Gulitskiy1Maria M. Kostenko2Tomáš Lučivjanský3Department of Physics, Saint-Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034, RussiaDepartment of Physics, Saint-Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034, RussiaDepartment of Physics, Saint-Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034, RussiaFaculty of Sciences, Safarik University, Moyzesova 16, 040 01 Košice, SlovakiaThe renormalization group approach and the operator product expansion technique are applied to the model of a passively advected vector field by a turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered in the vicinity of space dimension d = 4 and the perturbation theory is constructed within a double expansion scheme in y and ε = 4 − d , where y describes scaling behaviour of the random force that enters the Navier-Stokes equation. The properties of the correlation functions are investigated, and anomalous scaling and multifractal behaviour are established. All calculations are performed in the leading order of y, ε expansion (one-loop approximation).http://www.mdpi.com/2218-1997/5/1/37fully developed turbulencemagnetohydrodynamicsfield-theoretic renormalization groupanomalous scaling |
| spellingShingle | Nikolay V. Antonov Nikolay M. Gulitskiy Maria M. Kostenko Tomáš Lučivjanský Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4 † Universe fully developed turbulence magnetohydrodynamics field-theoretic renormalization group anomalous scaling |
| title | Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4 † |
| title_full | Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4 † |
| title_fullStr | Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4 † |
| title_full_unstemmed | Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4 † |
| title_short | Passive Advection of a Vector Field by Compressible Turbulent Flow: Renormalizations Group Analysis near d = 4 † |
| title_sort | passive advection of a vector field by compressible turbulent flow renormalizations group analysis near d 4 † |
| topic | fully developed turbulence magnetohydrodynamics field-theoretic renormalization group anomalous scaling |
| url | http://www.mdpi.com/2218-1997/5/1/37 |
| work_keys_str_mv | AT nikolayvantonov passiveadvectionofavectorfieldbycompressibleturbulentflowrenormalizationsgroupanalysisneard4 AT nikolaymgulitskiy passiveadvectionofavectorfieldbycompressibleturbulentflowrenormalizationsgroupanalysisneard4 AT mariamkostenko passiveadvectionofavectorfieldbycompressibleturbulentflowrenormalizationsgroupanalysisneard4 AT tomaslucivjansky passiveadvectionofavectorfieldbycompressibleturbulentflowrenormalizationsgroupanalysisneard4 |