Dynamics and Instabilities of Vortex Pairs

Abstract

This article reviews the characteristics and behavior of counter-rotating and corotating vortex pairs, which are seemingly simple flow configurations yet immensely rich in phenomena. Since the reviews in this journal by Widnall (1975) and Spalart (1998), who studied the fundamental structure and dynamics of vortices and airplane trailing vortices, respectively, there have been many analytical, computational, and experimental studies of vortex pair flows. We discuss two-dimensional dynamics, including the merging of same-sign vortices and the interaction with the mutually induced strain, as well as three-dimensional displacement and core instabilities resulting from this interaction. Flows subject to combined instabilities are also considered, in particular the impingement of opposite-sign vortices on a ground plane. We emphasize the physical mechanisms responsible for the flow phenomena and clearly present the key results that are useful to the reader for predicting the dynamics and instabilities of parallel vortices.

Two- and three-dimensional wake transitions of an impulsively started uniformly rolling circular cylinder

“…The results of So et al (2011) can be used to obtain an estimate for the most unstable wavelength. A recent review of the Crow instability is given in Leweke et al (2016). Examining the spanwise perturbation vorticity field of mode 5 (not shown) shows the characteristic lobe structure of Crow instability in the vortex pair as it moves away from the cylinder and the wall.…”

Afterbody vortices of axisymmetric cylinders with a slanted base

“…The ratio of the vortex core radius r core to the vortex separation distance b is around r core /b ≈ 0.2. According to Leweke et al (2016), both long wavelength and short wavelength instabilities can be amplified for this aspect ratio. To investigate possible time-dependent interactions of the vortex pair, instantaneous vortex locations in the crossflow plane were analyzed.…”

Vortex particle-mesh simulations of vertical axis wind turbine flows: from the airfoil performance to the very far wake

“…4a and isolated in Fig. 5, is well known in vortex dynamics and has already been identified on aircraft wakes (Bristol et al, 2004;Leweke et al, 2016). As a direct consequence, the turbulent regions of the wake grow from the corners and the wake only reaches a fully turbulent state once these regions have merged: the distance to reach this state will be governed directly by the aspect ratio of the machine.…”