A Definition of swirl function and identification of swirling flow

A method of identification of swirling flow (vortex) with definition of swirl function is presented. In fluid motion, eigenvalue of velocity gradient tensor classifies flow characteristic, and a complex (conjugate) eigenvalue indicates that flow is swirling motion (vortex) around the point as its axis. The imaginary part represents its angular velocity of swirling, and is Galilean invariant. This quantity is defined as swirl function as a physical property. The swirl function is a function of flow field where velocity field is defined, and the local maximum point of swirling function can be considered as its axis in finite swirling (vortical) region. Then an identification method with distribution of swirl function is developped, as SWANA2 code. This analysis is appropriate to estimate both location and intensity of swirling, and can identify vortex which the second invariant of velocity gradient tensor can not identify. SWANA2 is verified with Burgers vortex with uniform flow, and an application in CFD (Computational Fluid Dynamics) and experiment shows that this code can identify swirling motion with concrete vortical structure of velocity even in the case that swirling motion is hidden in uniform velocity or that flow visualization (streamline) indicates swirling location different from the correct swirling region