Vorticity Curvature Criterion for Two-Dimensional Vortex Identification

Vortical structures are an emblematic feature of turbulent flow, and, recently, due to better experimental techniques and computer simulations there is a growing interest in vortical, and, more generally, coherent structures in turblent fluid flow[1]. Systematic procedures for the identification of vortices/coherent structures have been proposed as a way to address their kinematical and dynamical roles in structural formulations of turbulence[2]. As a general rule, all of the known vortex detection algorithms are plagued with shortcomings[3]. In this work, we focus on one of the most popular methods - the swirling strength criterion - and investigate how it performs in controled Monte-Carlo tests. We, then, emphasize its main problematic issues: (i) vortex deformation and suppression due to the near presence of intense vortical structures; (ii) vortex merging; (iii) spuriuos vortices created in many-vortex configurations and (iv) in the presence of background shear. The inner layer of turbulent boundary layer flows is, in particular, the region where the swirling strength criterion looses accuracy in a dramatic way. We propose an alternative vortex detection criterion, based on the curvature properties of the vorticity profile, which clearly improves over the results obtained with the swirling strength criterion in a number of relevant case studies.

Bibliography:

[1] D. Dennis, Anais da Academia Brasileira de Ci?ncias 2015
[2] Moriconi, L., Phys. Rev. E 79/4, 2009
[3] Jeffrey A. LeHew et al., Caltech Ph.D thesis, 2012