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Definitions of vortex vector and vortex

Published online by Cambridge University Press:  18 June 2018

Shuling Tian Open the ORCID record for Shuling Tian [Opens in a new window] ,
Yisheng Gao ,
Xiangrui Dong  and
Chaoqun Liu Open the ORCID record for Chaoqun Liu [Opens in a new window]
Shuling Tian
Affiliation:
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
Yisheng Gao
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
Xiangrui Dong
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA National Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China
Chaoqun Liu*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
*
†Email address for correspondence: [email protected]
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Abstract

Although the vortex is ubiquitous in nature, its definition is somewhat ambiguous in the field of fluid dynamics. In this absence of a rigorous mathematical definition, considerable confusion appears to exist in visualizing and understanding the coherent vortical structures in turbulence. Cited in the previous studies, a vortex cannot be fully described by vorticity, and vorticity should be further decomposed into a rotational and a non-rotational part to represent the rotation and the shear, respectively. In this paper, we introduce several new concepts, including local fluid rotation at a point and the direction of the local fluid rotation axis. The direction and the strength of local fluid rotation are examined by investigating the kinematics of the fluid element in two- and three-dimensional flows. A new vector quantity, which is called the vortex vector in this paper, is defined to describe the local fluid rotation and it is the rotational part of the vorticity. This can be understood as that the direction of the vortex vector is equivalent to the direction of the local fluid rotation axis, and the magnitude of vortex vector is the strength of the location fluid rotation. With these new revelations, a vortex is defined as a connected region where the vortex vector is not zero. In addition, through direct numerical simulation (DNS) and large eddy simulation (LES) examples, it is demonstrated that the newly defined vortex vector can fully describe the complex vertical structures of turbulence.

JFM classification

Vortex Flows: Contour dynamics Mathematical Foundations: Topological fluid dynamics Vortex Flows: Vortex Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 849 , 25 August 2018 , pp. 312 - 339
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Copyright
© 2018 Cambridge University Press 

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