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 ...
[view complete introduction]

US $

*(Excluding Mailing and Handling)

Comparison of Liutex and Eigenvalue-based Vortex Identification Criteria for Compressible Flows

Pp. 154-175 (22)

Yisheng Gao and Chaoqun Liu


Currently, the Q criterion, theΔ criterion and the λci criterion are representative among the most widely used vortex identification criteria. These criteria can be categorized as eigenvalue-based criteria since they are exclusively determined by the eigenvalues or invariants of the velocity gradient tensor. However, these criteria are not always satisfactory and suffer from several defects, such as inadequacy of identifying the rotational axis and contamination by shearing. Recently, a novel concept of Liutex (previously named Rortex), including the scalar, vector and tensor form, was proposed to overcome the issues associated with the eigenvalue-based criteria. In the present paper, the comparison of Liutex and two eigenvalue-based criteria, namely the λ ci criterion and the QD criterion, a modification of the Q criterion, is performed to assess these methods for compressible flows. According to the analysis of the deviatoric part of the velocity gradient tensor, all the scalar, vector and tensor forms of Liutex are valid for compressible flows without any modification, while two eigenvalue-based criteria, though applicable to compressible flows, will tend to be severely contaminated by shearing as for incompressible flows. Vortical structures induced by supersonic microramp vortex generator (MVG) at Mach 2.5 are examined to confirm the validity and superiority of Liutex for compressible flows.


Compressible flows, Liutex/Rortex, Vortex identification, Vortex structures, Turbulence.


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