Comparative assessment and analysis of rorticity by Rortex in swirling jets Nan Gui 1 , Liang Ge 1 , Peng-xin Cheng 1 , Xing-tuan Yang 1 , Ji-yuan Tu 1, 2 , Sheng-yao Jiang 1 , 1. Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing, 100084, China 2. School of Engineering, RMIT University, Melbourne, VIC 3083, Australia (Received November 21, 2018, Revised December 21, 2018, Accepted January 23, 2019, Published online April 28, 2019) ©China Ship Scientific Research Center 2019 Abstract: Recently, a new definition, called rortex, has been proposed to quantify the purely rotational motion of fluids. In this work, based on the DNS data we employed the rortex to assess and visualize the rotational motion and structure of vortex in swirling jets in comparison with other kinds of vortex criteria of Q, λ 2 , vorticity and Omega. The rortex vector, Omega, Q, and λ 2 criteria are found to be better than vorticity for vortex core identification. The vector triangle formed by the Rortex R, nonrotational shear S, and vorticity  V is analyzed to give mechanical explanations, especially on the effect of non-rotational shear on rotation of fluids. In addition, the probability density distributions (PDF) of Rortex R, nonrotational shear S, and vorticity  V have been computed. The peak value of PDF of vorticity could be used to explain the pure rigid rotation effect and combination effects of rigid rotation and non-rotational shear. Key words: swirling flow, vortex, Rortex, direct numerical simulation, rigid rotation, non-rotational shear Introduction As well-known, identification of vortex plays an important role in studying the feature of fluid flow and uncovering the mechanisms of turbulence. The most conventional definition of vortex  V is based on the curl of fluid velocity V, i.e. = , V    V V V   (1) where  V is called vorticity. Hence, a connected fluid region with | V | > 0 is regarded as vortex. More recently, based on the work of Chong [1] , supposing V is the local velocity gradient tensor, solving the * Project supported by the National Natural Science Foundations of China (Grant No. 51576211), the Science Fund for Creative Research Groups of National Natural Science Foundation of China (Grant No. 51321002), the National High Technology Research and Development Program of China (863) (2014AA052701), and the Foundation for the Author of National Excellent Doctoral Dissertation of PR China (FANEDD, Grant No. 201438). Biography: Nan Gui (1982-), Male, Ph. D., Associate Professor, E-mail: guinan@mail.tsinghua.edu.cn Corresponding author: Shengyao Jiang, E-mail: shengyaojiang@tsinghua.edu.cn characteristic equation of it 3 2 2 0 1 [ ], ( [ ]), det( ) 2 P Q R P tr Q P tr R                    V V V (2) generates three eigenvalues λ i , (i=1,2,3). Many new definitions of vortex identification criteria have been proposed based on Eq. (2), such as the  Q-vortex [2] : It is defined by the positive second invariant 1 ( ) 2 Q   A B , where A and B are the symmetric and anti-symmetric parts of the velocity gradient tensor V . Q represents the balance between the shear strain rate and vorticity magnitude.  λ 2 -vortex [3] : To avoid complex eigenvalues, Jeong and Hussain [3] defined the λ 2 -vortex by the characteristic equation of 2 2  A B . The connected region with the secondly large eigenvalue λ 2 less than zero, i.e. λ 2 < 0, is regarded as vortex. Available online at https://link.springer.com/journal/42241 http://www.jhydrodynamics.com Journal of Hydrodynamics, 2019 https://doi.org/10.1007/s42241-019-0042-0