A method for characterizing cross-sections of vortices in turbulent flows

Highlights: ► We present a method for characterizing vortex cross-sections in turbulent flows. ► It is much less contaminated by shear than the existing methods. ► It is also simple, robust, and not selective (no vortices rejected). ► It uses a rigid-body-rotation vorticity (local triple-decomposition of motion). ► We show that λci is strongly contaminated by shear in turbulent flows. - Abstract: This paper describes a new method for characterizing cross-sections of vortices in turbulent flows that is simple, robust, not selective, and above all, much less contaminated by shear than the existing methods. By relying on the approach of Kolář (Int. J. Heat Fluid Flow 28, 2007) for separating swirling motions of vortices from pure shearing motions, the method computes a rigid-body-rotation vorticity that is not significantly contaminated by shear and that serves as the local measure of vortex-related vorticity. The effective radius and circulation of all detected vortices are determined by using this rigid-body-rotation vorticity in conjunction with the Gaussian vorticity distribution common to both the Oseen vortex and the Burgers vortex as a vortex template. Even if a template is necessary, no vortices are rejected because of their shape or their vorticity distribution. The errors in radius and circulation caused by the use of a vortex template in the method are analyzed with a quasi-elliptical vortex model. The advantages and limitations of this vortex characterization method are presented in detail. A wall-bounded turbulent flow is studied and it is shown that vortices are frequently in zones of strong instantaneous shear. Based on this result, we demonstrate that, contrary to rigid-body-rotation vorticity, the two commonly used measures of the local swirling rate of a vortex, vorticity and the imaginary part of the complex eigenvalues of the velocity gradient tensor λci, are strongly contaminated by shear. Hence, circulation or any vortex strength parameter directly derived from vorticity or λci is not accurate. The main interest of the present vortex characterization method is that it overcomes this problem.