Vortex and the Balance between Vorticity and Strain Rate

A new analysis of the vortex-identification Q-criterion and its recent modifications is presented. In this unified framework based on different approaches to averaging of the cross-sectional balance between vorticity and strain rate in 3D, new relations among the existing modifications are derived. In addition, a new method based on spherical averaging is proposed. It is applicable to compressible flows, and it inherits a duality property which allows its use for identifying high strain-rate zones together with vortices. The new quantity is applied to identification of vortices and high strain-rate zones in the flow around an inclined flat plate, in the flow past a sphere, and for the reconnection process of two Burgers vortices.