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• Turbulent transition must be promoted by transforming anti-symmetric shear to rotation. • Volume Liutex can quantitatively evaluate the degree of turbulence and transition. • The fluctuation of the laminar flow transition is mainly caused by the flow rotation. • Reynolds stress concentrates in the surrounding of vortex core with high Liutex inside. Correlation analysis on the vorticity, Liutex and the anti-symmetric shear, is discussed in this paper based on the new introduced vortex definition of Liutex, to explore the mechanism of the vortex generation in laminar flow transition and the relation between the fluctuation and the rotation. Compared with the volume vorticity as a good measurement to evaluate the statistical fluctuations, a new concept named volume Liutex is introduced in this study to predict the turbulence, which is an accurate yardstick to quantitatively evaluate the degree of the transition from laminar flow to turbulence. A relatively high correlation between the fluctuation and the rotation is discovered in the transitional flow. It is found that the laminar flow transition must be promoted by transforming the anti-symmetric shear to the rotation; the fluctuation of the flow in transition is mainly caused by the flow rotation, or, the turbulence is caused by Liutex generation and growth. In addition, the Reynolds stress is found concentrated in the surrounding area of the vortex core which has a high Liutex value inside. [ABSTRACT FROM AUTHOR]