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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New Omega Vortex Identification Method Based on Determined Epsilon

Pp. 45-58 (14)

Xiangrui Dong, Yisheng Gao and Chaoqun Liu


A new Omega (Ω) method with ε determination is introduced to represent the ratio of vorticity square over the sum of vorticity squared and deformation squared, for vortex identification. the advantages of the new Ω method can be summarized as follows: (1) Ω, as a ratio of the vorticity squared over the sum of the vorticity squared and deformation squared, is a normalized and case-independent function which satisfies Ω ∈[0,1]; (2) Compared with the other vortex visualization methods, which require a wide threshold to capture the vortex structures, Ω can always be set as 0.52 to capture vortex for different cases and time steps; (3) ε is defined as a function without any adjustment on its coefficient for all cases; (4) The Ω method can capture both strong and weak vortices simultaneously. In addition, Ω is quite robust with no obvious change in vortex visualization.


Case-independent, Deformation, Omega method, Vortex identification, Vorticity.


Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019, USA