International Conference on Liutex Theory and Turbulence Mechanism (LIUTEX2026)

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Glossary

1

Liutex

A third-generation vortex-identification quantity derived from the real eigenvector of the velocity-gradient tensor. The eigenvector gives the local rotation axis and the Liutex magnitude R measures the strength of rigid-body-like rotation about that axis, giving both a direction and a scalar for the vortex.

2

Rortex

The earlier name used for the Liutex vector in the original publications; Rortex denotes the vector form and Liutex the rotation axis plus magnitude formulation. Both describe the rigid rotational part of fluid motion isolated from shear.

3

Vorticity

The curl of the velocity field. It measures local rotation but is also generated by shear and stretching, so high vorticity does not always mean a vortex - the main motivation for the second- and third-generation criteria.

4

Q-criterion

Second invariant of the velocity-gradient tensor, Q = 0.5 x (||Omega||^2 - ||S||^2). A region is flagged as a vortex where Q is positive, that is where rotation dominates strain.

5

Lambda2 criterion

Vortex identified where the second eigenvalue of the symmetric tensor S^2 + Omega^2 is negative. It removes the local pressure contribution and is widely used for iso-surface rendering in CFD post-processors.

6

Delta criterion

Vortex region defined where the discriminant of the characteristic equation of the velocity-gradient tensor is positive, meaning the tensor has complex eigenvalues and the local streamline pattern is closed or spiralling.

7

Omega method

Ratio of vorticity squared to the sum of vorticity squared and strain-rate squared, plus a small positive number to avoid division by zero. A common threshold is about 0.52; the method is threshold-sensitive and has Liutex-based variants such as Omega_R.

8

Velocity-gradient tensor

The 3x3 matrix of partial derivatives of velocity. Its eigenvalues and eigenvectors determine local flow topology and underpin every vortex-identification criterion discussed at the summit.

9

Triple decomposition

Splitting of the velocity-gradient tensor into rigid-body rotation, pure shear and normal stretching parts. The Liutex derivation uses this decomposition to isolate the rotational component from shear.

10

Third-generation vortex identification

Methods that return both a vortex vector (axis and direction) and a magnitude. First generation covers vorticity, second generation covers scalar criteria such as Q, lambda2 and Delta, and third generation covers Liutex, Rortex and their variants.

11

Vortex boundary

The iso-surface or threshold that separates vortex from non-vortex fluid for a chosen criterion. Liutex-based boundaries are usually described as more stable across thresholds than Q or Omega contours.

12

Galilean invariance

The requirement that identification results do not change when the reference frame moves at constant velocity. Criteria that fail this test can label the same structure differently depending on frame choice.

13

Particle image velocimetry (PIV)

Whole-field optical measurement that tracks seeded particles between laser pulses to reconstruct instantaneous velocity fields, from which velocity-gradient tensors and vortex criteria can be computed experimentally.

14

Large-eddy and direct numerical simulation (LES, DNS)

Scale-resolving CFD approaches that capture the unsteady structures vortex criteria are designed to describe. Both generate the large velocity-gradient datasets that dominate post-processing workloads at vortex-focused meetings.