Simulation of vortex reconnection (original) (raw)

Incompressible hydrodynamic turbulence from a chain reaction of vortex reconnection events

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...

Vortex Ring Reconnections

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.

Compressible vortex reconnection

Journal of Fluid Mechanics, 1995

Reconnection of two antiparallel vortex tubes is studied as a prototypical coherent structure interaction to quantify compressibility effects in vorticity dynamics. Direct numerical simulations of the Navier-Stokes equations for a perfect gas are carried out with initially polytropically related pressure and density fields. For an initial Reynolds number (Re = Γ /v, circulation divided by the kinematic viscosity) of 1000, the pointwise initial maximum Mach number (M) is varied from 0.5 to 1.45. At M=0.5, not surprisingly, the dynamics are essentially incompressible. As M increases, the transfer of Γ starts earlier. For the highest M, we find that shocklet formation between the two vortex tubes enhances early Γ transfer due to viscous cross-diffusion as well as baroclinic vorticity generation. The reconnection at later times occurs primarily due to viscous cross-diffusion for all M. However, with increasing M, the higher early Γ transfer reduces the vortices’ curvature growth and hen...

Analysis of Reynolds number scaling for viscous vortex reconnection

Physics of Fluids, 2012

We study reconnections of quantum vortices by numerically solving the governing Gross-Pitaevskii equation. We find that the minimum distance between vortices scales differently with time before and after the vortex reconnection. We also compute vortex reconnections using the Biot-Savart law for vortex filaments of infinitesimal thickness, and find that, in this model, reconnections are time symmetric. We argue that the likely cause of the difference between the Gross-Pitaevskii model and the Biot-Savart model is the intense rarefaction wave which is radiated away from a Gross-Pitaeveskii reconnection. Finally we compare our results to experimental observations in superfluid helium and discuss the different length scales probed by the two models and by experiments.

Fully Developed Hydrodynamic Turbulence from a Chain Reaction of Reconnection Events

Procedia IUTAM, 2013

From a new anti-parallel initial condition using long vortices, three-dimensional incompressible turbulence forms after two reconnection steps and the formation of at least one set of vortex rings, similar to how anti-parallel quantum vortices evolve [10]. The long domain allows multiple reconnections, which enhance vortex stretching rates and the generation of small-scale vortex structures within the vortex rings. For the Navier-Stokes vortices, further new features are a profile less likely to shed vortex sheets and an improved mapping of the direction of the vorticity onto the three-dimensional mesh. The vortices evolve via the following steps: First, until the first reconnection, dynamics largely consistent with how vortices attract in the Euler equations. Second, vortex reconnection where the symmetry planes meet. Third, a series of vortex rings, with the stretching at each following set of reconnections leading to the new reconnections and rings. Roughly half of the circulation reconnects into two "bridges", leaving two distinct "threads", as he extra stretching transforms the threads into spirals wrapped around the bridges. It is argued that these spirals are the source of the observed k −5/3 energy spectra and other statistics commonly associated with high Reynolds number turbulence.

Reconnection of colliding vortex rings

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.

Vortex reconnection in the late transition in channel flow

Vortex reconnection, as the topological change of vortex lines or surfaces, is a critical process in transitional flows, but is challenging to accurately characterize, particularly in shear flows. We apply the vortex-surface field (VSF), whose isosurface is the vortex surface consisting of vortex lines, to study vortex reconnection in the Klebanoff-type temporal transition in channel flow. The VSF evolution can capture the reconnection of the hairpin-like vortical structures evolving from the initial vortex sheets in opposite halves of the channel. The incipient vortex reconnection is characterized by the vanishing minimum distance between a pair of vortex surfaces and the reduction of vorticity flux through the region enclosed by the wall and the VSF isoline of the channel half-height on the spanwise symmetric plane. We find that the surge of the wall-friction coefficient begins at the identified reconnection time. From the Biot–Savart law, the rapid reconnection of vortex lines can induce a velocity opposed to the mean flow, which partially blocks the flow near the central region and generally accelerates the near-wall fluid motion in the flow with constant mass flux. Therefore, the vortex reconnection appears to play an important role in the sudden increase of wall friction in transitional channel flows.

Dynamics of Quantized Vortices Before Reconnection

Journal of Low Temperature Physics, 2016

The main goal of this paper is to investigate numerically the dynamics of quantized vortex loops, just before the reconnection at finite temperature, when mutual friction essentially changes evolution of lines. Modeling is performed on the base of vortex filament method with using the full Biot-Savart equation. It was discovered that initial position of vortices and the temperature strongly affect the dependence on time of the minimum distance δ(t) between tips of two vortex loops. In particular, in some cases the shrinking and collapse of vortex loops due to mutual friction occur earlier than reconnection, thereby cancelling the latter. However, this relationship takes a universal square-root form δ (t) = (κ/2π) (t * − t) at distances smaller than the one, satisfying the Schwarz criterion, when nonlocal contribution to the Biot-Savart equation becomes about equal to local contribution. In the "universal" the nearest parts of vortices form a pyramid-like structure with angles which are also don't depend both on the initial configuration of filaments and on the temperature. Keywords superfluid helium • quantized vortices • shrinking • vortex filament method • Biot-Savart equation This work was supported by RFBR grants No.