Low-Order Moments of Velocity Gradient Tensors in Two-Dimensional Isotropic Turbulence
In isotropic turbulence, symmetry of different directions can reduce the number of independent components for velocity gradient tensors. In three-dimensional isotropic turbulence, the independent components under either incompressible or compressible conditions have already been analyzed in the lite...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/16/2/175 |
| _version_ | 1797296966272548864 |
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| author | Chensheng Luo Ping-Fan Yang Le Fang |
| author_facet | Chensheng Luo Ping-Fan Yang Le Fang |
| author_sort | Chensheng Luo |
| collection | DOAJ |
| description | In isotropic turbulence, symmetry of different directions can reduce the number of independent components for velocity gradient tensors. In three-dimensional isotropic turbulence, the independent components under either incompressible or compressible conditions have already been analyzed in the literature. However, for two-dimensional isotropic turbulence, they are still unclear. We derive rigorously the independent components for velocity gradient tensors of two-dimensional isotropic turbulence and give physical explanations. These theoretical results are validated using high-resolution direct numerical simulations (DNSs) of two-dimensional compressible turbulence. Results show that the present DNS setup is still not sufficient to capture the isotropy of third-order moments, suggesting that more investigations on determining the smallest scale and improving the numerical schemes for two-dimensional compressible turbulence are required. |
| first_indexed | 2024-03-07T22:12:29Z |
| format | Article |
| id | doaj.art-d7f658f493e3455b86cdb06fe896a48a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-07T22:12:29Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-d7f658f493e3455b86cdb06fe896a48a2024-02-23T15:35:55ZengMDPI AGSymmetry2073-89942024-02-0116217510.3390/sym16020175Low-Order Moments of Velocity Gradient Tensors in Two-Dimensional Isotropic TurbulenceChensheng Luo0Ping-Fan Yang1Le Fang2Laboratory of Complex System, Ecole Centrale de Pékin/School of General Engineering, Beihang University, Beijing 100191, ChinaThe State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, ChinaLaboratory of Complex System, Ecole Centrale de Pékin/School of General Engineering, Beihang University, Beijing 100191, ChinaIn isotropic turbulence, symmetry of different directions can reduce the number of independent components for velocity gradient tensors. In three-dimensional isotropic turbulence, the independent components under either incompressible or compressible conditions have already been analyzed in the literature. However, for two-dimensional isotropic turbulence, they are still unclear. We derive rigorously the independent components for velocity gradient tensors of two-dimensional isotropic turbulence and give physical explanations. These theoretical results are validated using high-resolution direct numerical simulations (DNSs) of two-dimensional compressible turbulence. Results show that the present DNS setup is still not sufficient to capture the isotropy of third-order moments, suggesting that more investigations on determining the smallest scale and improving the numerical schemes for two-dimensional compressible turbulence are required.https://www.mdpi.com/2073-8994/16/2/175two-dimensional turbulencecompressible turbulencevelocity gradient |
| spellingShingle | Chensheng Luo Ping-Fan Yang Le Fang Low-Order Moments of Velocity Gradient Tensors in Two-Dimensional Isotropic Turbulence Symmetry two-dimensional turbulence compressible turbulence velocity gradient |
| title | Low-Order Moments of Velocity Gradient Tensors in Two-Dimensional Isotropic Turbulence |
| title_full | Low-Order Moments of Velocity Gradient Tensors in Two-Dimensional Isotropic Turbulence |
| title_fullStr | Low-Order Moments of Velocity Gradient Tensors in Two-Dimensional Isotropic Turbulence |
| title_full_unstemmed | Low-Order Moments of Velocity Gradient Tensors in Two-Dimensional Isotropic Turbulence |
| title_short | Low-Order Moments of Velocity Gradient Tensors in Two-Dimensional Isotropic Turbulence |
| title_sort | low order moments of velocity gradient tensors in two dimensional isotropic turbulence |
| topic | two-dimensional turbulence compressible turbulence velocity gradient |
| url | https://www.mdpi.com/2073-8994/16/2/175 |
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