Current Developments in Mathematical Sciences

Current Developments in Mathematical Sciences

Volume: 2

Liutex-based and Other Mathematical, Computational and Experimental Methods for Turbulence Structure

The knowledge of quantitative turbulence mechanics relies heavily upon the definition of the concept of a vortex in mathematical terms. This reference work introduces the reader to Liutex, which is ...
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Liutex and Its Calculation and Galilean Invariance

Pp. 21-44 (24)

Yiqian Wang, Yisheng Gao and Chaoqun Liu


The Liutex (previously known Rortex) method introduces a vortex vector field to mathematically and systematically describe vortices in flow fields. In this study, the previous calculation procedures of Liutex which includes a two-step reference coordinate rotation is revisited first. An explicit formula to calculate Liutex is then derived and the physical intuition and efficiency improvement brought by this formula are discussed. It is estimated that the computation time of Liutex vector from velocity gradient field can be reduced by 36.6% compared with that of the previous method. Besides, the Galilean invariance widely accepted as a preliminary check for a successful vortex identification method is discussed for Liutex vector.


Angular velocity, Coherent structures, Galilean invariance, Liutex, Vortex identification, Velocity gradient tensor.


School of Mathematical Science, Soochow University, Suzhou 215006, China.