Interaction of unequal anti-parallel vortex tubes

Experimental Thermal and Fluid Science, 2017

The interactions between two streamwise vortices were investigated by wind tunnel testing of two NACA0012 vanes at various lateral offsets. One vane was spaced 10 chord lengths (C) downstream of the other, with both at an angle of incidence of 8 degrees and a Reynolds number of 7 10 4. The evolution of the vortex pair was observed until 6.5C behind the downstream vane using Particle Image Velocimetry (PIV). It was found that proximity of the upstream vortex to the downstream vane had a significant effect on the rotational rate of the subsequent vortex pair, with far offset cases having little rotation, and near field cases having angle changes of 19.6 degrees per chord length travelled downstream. At the point of vortex impingement on the downstream vane, the rotational rate dropped to near zero due to a significant strength reduction of both vortices. The point of strongest interaction was found to be laterally offset from the point of closest vortex proximity to the downstream vane by 0.15C, with the vortex on the suction side of the vane. In the offset range investigated, a significant instability was observed in only the upstream vortex. These instabilities increased as the proximity between the vortices decreased, peaking where the vortex interaction was strongest.

Physics of Fluids, 2020

We formulate a system of equations that describe the motion of four vortices made up of two interacting vortex pairs, where the absolute strengths of the pairs are different. Each vortex pair moves along the same axis in the same sense. In much of the literature, the vortex pairs have equal strength. The vortex pairs can either escape to infinite separation or undergo a periodic leapfrogging motion. We determine an explicit criterion in terms of the initial horizontal separation of the vortex pairs given as a function of the ratio of their strengths to describe a periodic leapfrogging motion when interacting along the line of symmetry. In the Appendix, we also contrast a special case of interaction of a vortex pair with a single vortex of the same strength in which a vortex exchange occurs.

2004

We present a combined analytical and numerical study of the instabilities of a pair of parallel unequal-strength vortices. We extend the analyses of a vortex in an external strain field (Crow,

The two-and three-dimensional interactions of a pair of co-rotating vortices, representing a simplified model of flows found in the extended near wake behind aircraft wings, are analyzed using water tank experiments and numerical simulations. At low Reynolds numbers (Re), the vortices undergo two-dimensional merging, when the core size exceeds a certain fraction of the vortex separation distance. The time it takes to reach this limit increases with Re. At higher Re, a three-dimensional instability is observed, showing the characteristics of an elliptic instability of the vortex cores. The spatial structure of the amplified unstable modes, as well as their growth rate as function of axial wavelength are given and compared to theoretical predictions, showing excellent agreement between the three approaches. The instability is found to rapidly generate small-scale motion, initiating merging for smaller core sizes and producing a turbulent final vortex.

Journal of Fluid Mechanics, 1991

The interaction of two identical circular viscous vortex rings starting in a side-byside configuration is investigated by solving the Navier-Stokes equation using a spectral method with 643 grid points. This study covers initial Reynolds numbers (ratio of circulation to viscosity) up to 1153. The vortices undergo two successive reconnections, fusion and jhsion, as has been visualized experimentally, but the simulation shows topological details not observed in experiments. The shapes of the evolving vortex rings are different for different initial conditions, but the mechanism of the reconnection is explained by bridging ) except that the bridges are created on the front of the dipole close to the position of the maximum strain rate. Spatial structures of various field quantities are compared. It is found that domains of high energy dissipation and high enstrophy production overlap, and that they are highly localized in space compared with the regions of concentrated vorticity. The kinetic energy decays according to the same power laws as found in fully developed turbulence, consistent with concentrated regions of energy dissipation. The main vortex cores survive for a relatively long time. On the other hand, the helicity density which is higher in roots of bridges and threads (or legs) changes rapidly in time. The high-helicity-density and high-energy-dissipation regions overlap significantly although their peaks do not always do so. Thus a longlived structure may carry high-vorticity rather than necessarily high-helicity density. It is shown that the time evolution of concentration of a passive scalar is quite different from that of the vorticity field, confirming our longstanding warning against relying too heavily on flow visualization in laboratory experiments for studying vortex dynamics and coherent structures.

Physical review fluids, 2021

2002

We investigate numerically the Navier-Stokes dynamics of reconnecting vortex rings at small Re number. We find that reconnections are dissipative due to the smoothing of vorticity gradients at reconnection kinks and to the formation of secondary structures of stretched anti-parallel vorticity which transfer kinetic energy to small scales where it is subsequently dissipated efficiently. In addition, the relaxation of the reconnection kinks excites Kelvin waves which due to strong damping are of low wavenumber and affect directly only large scale properties of the flow. PACS numbers: 47.32.Cc, 02.70.Ns In flow phenomena as diverse as quantum [1] magnetic [2] and incompressible [3] fluids, it is useful to study the physics of turbulence by modeling the system as a collection of tubular flux loops which in the case of vortical fields are called vortex filaments. An intrinsic property of such highly structured systems is their ability to dynamically change their topology via reconnection mechanisms. Does this change in topology affect in turn properties of fluid turbulence like the intermittency and the scalar-mixing (which depend directly on the structure of the flow) or like the dynamics of energy in wavenumber space? Or is it the case that reconnection events are not generic and thus have no direct impact on the mean properties of turbulent flows? The aim of this letter is to address these issues by fully resolving the Navier-Stokes dynamics of interacting vortex rings for three simple geometries having great potential for illuminating the physics of reconnection. Although the flows considered are not strictly turbulent, the hope is that in a future structural approach to the problem of turbulence a significant part of the flow complexity could be traced back to the physics of similar vortex interactions. Incompressible vortex reconnections have an extensive bibliography (for a review of the work up to 1994, see ). In reconnections of vortex tubes were considered with an emphasis on the possibility of singularity formation as Re → ∞. In [7] the strong interactions between vortex rings were computed with the interest in developing numerical methods and turbulence models rather than in focusing on the physics of reconnection. In it is discussed how a linked vortex configuration could be achieved starting from an unlinked initial state and in it is considered how the mixing of a nondiffusing passive scalar is affected during vortex ring collision. The reconnection of two approaching (but not colliding) vortex rings was studied experimentally in [10] and theoretically in . This letter extends these studies by considering generic vortex configurations and by capturing more features of vortex reconnections in a turbulent flow.

2008

From a new anti-parallel initial condition using long vortices, three-dimensional turbulence forms after two reconnection steps and the formation of at least one vortex ring. The long domain is needed in order to accommodate the multiple reconnections, which enhance vortex stretching rates and the generation of small-scale vortex structures within the vortex rings. In addition to making the initial vortices very long, new features introduced with this initial condition are an initial profile less likely to shed vortex sheets and an improved method for mapping the direction of the vorticity onto the three-dimensional mesh. To get to the turbulent state, the vortices progress through the following steps: First, until the first reconnection, the vortex dynamics is largely consistent with existing work on strong, possibly singular, growth of the vorticity in the Euler equations. Second, vortex reconnection at the junction of the primary symmetry planes meet. About half of the circulatio...

We investigate numerically the Navier-Stokes dynamics of reconnecting vortex rings at small Reynolds number for a variety of configurations. We find that reconnections are dissipative due to the smoothing of vorticity gradients at reconnection kinks and to the formation of secondary structures of stretched antiparallel vorticity which transfer kinetic energy to small scales where it is subsequently dissipated efficiently. In addition, the relaxation of the reconnection kinks excites Kelvin waves which due to strong damping are of low wave number and affect directly only large scale properties of the flow.