Qcriterion

The Q-criterion is a method used in computational fluid dynamics to identify and visualize vortical structures within a flow field. It is based on the second invariant of the velocity gradient tensor. A key feature of the Q-criterion is that it defines regions of rotation as areas where the magnitude of the vorticity vector is locally greater than the magnitude of the strain rate tensor. Specifically, a region is considered vortical if Q > 0. This condition effectively separates regions dominated by rotation from those dominated by shear.

The mathematical formulation of the Q-criterion involves calculating the eigenvalues of the velocity gradient tensor. Where the imaginary parts of these eigenvalues are non-zero, it indicates rotation. The Q-criterion, however, provides a more direct and visually intuitive approach by focusing on the relative magnitudes of rotational and strain rates. It is widely used to identify coherent structures such as vortices, boundary layers, and shear layers in various flow simulations, from turbulent jets to atmospheric phenomena. Its simplicity and robustness make it a popular choice for flow visualization and analysis in research and engineering applications.