Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition
In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (Liu et al. 2018). It is...
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| Published in | Journal of hydrodynamics. Series B Vol. 31; no. 3; pp. 464 - 474 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Singapore
Springer Singapore
01.06.2019
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| Online Access | Get full text |
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| Abstract | In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (Liu et al. 2018). It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (
λ
ci
) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the Liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the Liutex vector. |
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| AbstractList | In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (Liu et al. 2018). It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (
λ
ci
) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the Liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the Liutex vector. |
| Author | Liu, Chaoqun Wang, Yi-qian Gao, Yi-sheng Liu, Jian-ming |
| Author_xml | – sequence: 1 givenname: Yi-qian surname: Wang fullname: Wang, Yi-qian organization: School of Aerospace Engineering, Tsinghua University – sequence: 2 givenname: Yi-sheng surname: Gao fullname: Gao, Yi-sheng organization: Department of Mathematics, University of Texas at Arlington – sequence: 3 givenname: Jian-ming surname: Liu fullname: Liu, Jian-ming organization: School of Mathematics and Statistics, Jiangsu Normal University – sequence: 4 givenname: Chaoqun surname: Liu fullname: Liu, Chaoqun email: cliu@uta.edu organization: Department of Mathematics, University of Texas at Arlington |
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| Copyright | China Ship Scientific Research Center 2019 |
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| Keywords | Liutex Liutex-Shear decomposition explicit formula of Liutex Vorticity |
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| Snippet | In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of... |
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| Title | Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition |
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