Q-criterion (CFD)

The Q-criterion identifies vortices in a CFD field as regions where the second invariant of the velocity-gradient tensor is positive, Q = 0.5(||Omega||^2 - ||S||^2) > 0, with Omega the rotation-rate tensor and S the strain-rate tensor. A positive Q means local rotation dominates strain, the condition for a coherent vortex. Hunt, Wray, and Moin proposed it in 1988. It is the standard way to visualize bilge vortices, propeller tip and hub vortices, and wake structures from RANS, DES, or LES solutions, drawn as isosurfaces of a chosen Q level. Because the threshold is arbitrary, it shows vortex topology rather than absolute strength.