Collision Of Vortex Rings Research Articles

Transient skin friction behavior associated with hemisphere-based vortex ring collisions

Global and local transient skin friction variations resulting from a large-eddy simulation study on ReΓ0=3000 vortex rings colliding with surface-mounted hemispheres of hemisphere-to-vortex-ring diameter-ratios of 0.5≤D/d≤2 are investigated here. Skin friction distribution changes due to the approaching primary vortex ring, formation of secondary/tertiary vortex rings, subsequent mutual interactions between various vortex ring structures, and azimuthal instabilities are clarified with a view to better establish their relationships when the relative hemisphere size varies. Results show that the primary vortex ring produces the highest skin friction levels when it is close to or collides with the hemisphere/flat wall. Additionally, entrainment of wavy secondary/tertiary vortex rings leads to them entangling around the primary vortex ring and resulting in segmented skin friction regions at later stages of the collision process, regardless of the diameter-ratio. Unlike smaller hemispheres, the largest D/d=2 hemisphere here restricts all skin friction changes along its surface with the flat wall unaffected. It is also revealed here that while the diameter-ratio governs the global skin friction distributions, how secondary/tertiary vortex rings interact with the primary vortex ring and how azimuthal instabilities manifest and evolve for all the various vortex rings confer strong influences on the breaking-up and dissipation of regions with high skin friction levels.

Flow transitions of head-on vortex ring collisions with contaminated air–water interfaces

An experimental study was conducted on head-on collisions of Re = 2000 and 4000 vortex rings upon air–water interfaces to study the vortex dynamics and the effects of different vortex ring Reynolds numbers on the key vortex flow mechanisms. Unfiltered tap water was used where surface contaminants were present; hence, the interfacial stress levels are lower but not entirely zero like an idealized free surface. Results demonstrate that the vortex dynamics involve first, the resulting secondary and tertiary vortex rings transitioning into wavy states, before their upper loops disconnect/reconnect to the interface to form U-shaped vortex loops along the inner and outer peripheries of the primary vortex ring, respectively, in an alternating pattern. Second, tertiary vortex loops entangle around the primary vortex ring to produce counter-rotating vortex pairs that reorganize themselves along the primary vortex ring outer periphery, between the primary vortex ring and secondary vortex loops, as well as hairpin-like structures that aid ejection of primary vortex ring momentum. Third, secondary vortex loops rotate toward the collision axis before their lower segments are entrained by the primary vortex ring. A higher Reynolds number primary vortex ring would confer additional flow changes, such as a higher wave number for the secondary and tertiary vortex rings/loops, pairings of secondary vortex loops “side-arms” that reduce their instances by about half and formations of Tsai–Widnall–Moore–Saffman instabilities induced by flow perturbations. Finally, vortex flow models proposed to explain the flow mechanism at different flow stages are found to be in good agreements with the experimental visualizations.

Turbulence through sustained vortex ring collisions

Turbulence through sustained vortex ring collisions

Effect of shock tunnel geometry on shockwave and vortex ring formation, propagation, and head on collision

Vortex ring research primarily focuses on the formation from circular openings. Consequently, the role of tunnel geometry is less understood, despite there being numerous research studies using noncircular shock tunnels. This experimental study investigated shockwaves and vortex rings from different geometry shock tunnels from formation at the tunnel opening to head on collision with another similarly formed vortex ring using schlieren imaging and statistical analysis. The velocity of the incident shockwave was found to be consistent across all four shock tunnel geometries, which include circle, hexagon, square, and triangle of the same cross-sectional area. The velocity was 1.2 ± 0.007 Mach and was independent of the tunnel geometry. However, the velocities of the resulting vortex rings differed between the shapes, with statistical analysis indicating significant differences between the triangle and hexagon vortex velocities compared to the circle. Vortex rings from the square and circle shock tunnels were found to have statistically similar velocities. All vortex rings slowed as they traveled due to corner inversion and air drag. All shock tunnels with corners produce a wobble in the vortex rings. Vortex rings interact with opposing incident shockwaves prior to colliding with each other. Vortex velocity before and after shock–vortex interaction was measured and evaluated, showing statistically similar results. Shock–vortex interaction slows the shockwave upon interaction, while the shock–shock interaction resulted in no change in shock velocity. Although the vortex rings travel at different velocities, all head-on vortex ring collisions produce a perpendicular shockwave that travels at 1.04 ± 0.005 Mach.

Multi-resolution lattice Green's function method for incompressible flows

We propose a multi-resolution strategy that is compatible with the lattice Green's function (LGF) technique for solving viscous, incompressible flows on unbounded domains. The LGF method exploits the regularity of a finite-volume scheme on a formally unbounded Cartesian mesh to yield robust and computationally efficient solutions. The original method is spatially adaptive, but challenging to integrate with embedded mesh refinement as the underlying LGF is only defined for a fixed resolution. We present an ansatz for adaptive mesh refinement, where the solutions to the pressure Poisson equation are approximated using the LGF technique on a composite mesh constructed from a series of infinite lattices of differing resolution. To solve the incompressible Navier-Stokes equations, this is further combined with an integrating factor for the viscous terms and an appropriate Runge-Kutta scheme for the resulting differential-algebraic equations. The parallelized algorithm is verified through with numerical simulations of vortex rings, and the collision of vortex rings at high Reynolds number is simulated to demonstrate the reduction in computational cells achievable with both spatial and refinement adaptivity.

The influence of collision angle for viscous vortex reconnection

We revisit the mechanism of viscous vortex reconnection by considering the collision of vortex rings over a range of initial collision angles and Reynolds numbers. While the overall reconnection process is similar to anti-parallel vortex reconnection, we find that collision angle exerts significant influence over the process, altering the evolution of various global and local quantities. The collision angle primarily manipulates the “pyramid” process, a recently identified stretching mechanism proposed by Moffatt and Kimura [“Towards a finite-time singularity of the Navier-Stokes equations Part 1. Derivation and analysis of dynamical system,” J. Fluid Mech., 861, 930–967 (2019)] to be a potential pathway for finite-time singularity of Euler’s equations, during the approach stage of the rings. However, the “pyramid” process is short-lived for viscous vortices. The present work shows that the “pyramid” process is arrested by parallelization of the colliding vortices, wherein contact of the colliding vortices halts their motion toward each other at the pyramid apex, allowing the rest of the vortex tube to “catch up,” breaking the pyramid structure. Parallelization marks the transition to a second phase of stretching, where the colliding vortices remain parallel. Vorticity amplification from pyramid stretching is significantly stronger than for its parallel counterpart, and is thus the dominant factor determining reconnection properties. Based upon the findings in this study, we conjecture that the parallelization process is the primary mechanism that prevents the finite-time singularity through the pyramid process. Critically, the Reynolds number scaling for the reconnection rate differs depending on the collision angle, which challenges the conjecture of universal Reynolds number scaling in the literature.

Flow transitions in collisions between vortex-rings and density interfaces

Flow transitions and vortical developments during vortex-ring collisions with a sharp water–oil density interface are studied using planar laser-induced fluorescence and time-resolved particle-image velocimetry techniques. Circular vortex-rings at Reynolds numbers of $$\hbox {Re}=1000, 2000$$ and 4000 colliding with a density interface characterized by an Atwood number of approximately $$A=0.045$$ were investigated. Results show that at $$\hbox {Re}=1000$$ , collision with the density interface produces vortical structures and flow transitions that are relatively similar to those for a solid-boundary collision. However, the dynamics underlying the present vortical formations and behaviour are different from those associated with solid-boundary collisions, in that the former are driven by baroclinic vorticity generation. Flow behaviour at $$\hbox {Re}=2000$$ shows more significant deformation of the density interface by the vortex-ring but overall behaviour remains comparable. Last but not least, at $$\hbox {Re}=4000$$ , the largest Reynolds number investigated here, the vortex-ring penetrates the density interface almost completely. However, buoyancy effects eventually limit its penetration and reverse its translational direction, such that it crosses back into the oil layer again with its vortex core rotational senses reversed as well. At the same time, vortex-ring fluid is shed and a significant trailing-jet is left in the former’s wake.

Cascade leading to the emergence of small structures in vortex ring collisions

When vortex rings collide head-on at high enough Reynolds numbers, they ultimately annihilate through a violent interaction which breaks down their cores into a turbulent cloud. We experimentally show that this very strong interaction, which leads to the production of fluid motion at very fine scales, uncovers direct evidence of a novel iterative cascade of instabilities in a bulk fluid. When the coherent vortex cores approach each other, they deform into tent-like structures, and the mutual strain causes them to locally flatten into extremely thin vortex sheets. These sheets then break down into smaller secondary vortex filaments, which themselves rapidly flatten and break down into even smaller tertiary filaments. By performing numerical simulations of the full Navier-Stokes equations, we also resolve one iteration of this instability and highlight the subtle role that viscosity must play in the rupturing of a vortex sheet. The concurrence of this observed iterative cascade of instabilities over various scales with those of recent theoretical predictions could provide a new mechanistic framework in which the evolution of turbulent flows can be examined in real-time as a series of discrete dynamic instabilities.

Emergence of small scales in vortex ring collisions

This paper is associated with a video winner of a 2017 APS/DFD Gallery of Fluid Motion Award. The original video is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2017.GFM.V0037

A method to control and analyze vortex ring collisions in the laminar regime

Experimental physicists describe how complex laminar vortex ring collisions distribute their energy to produce diverse secondary rings.

Numerical Simulations of Two Coaxial Vortex Rings Head-on Collision

AbstractVortex rings have been a subject of interest in vortex dynamics due to a plethora of physical phenomena revealed by their motions and interactions within a boundary. The present paper is devoted to physics of a head-on collision of two vortex rings in three dimensional space, simulated with a second order finite volume scheme and compressible. The scheme combines non-iterative approximate Riemann-solver and piecewise-parabolic reconstruction used in inviscid flux evaluation procedure. The computational results of vortex ring collisions capture several distinctive phenomena. In the early stages of the simulation, the rings propagate under their own self-induced motion. As the rings approach each other, their radii increase, followed by stretching and merging during the collision. Later, the two rings have merged into a single doughnut-shaped structure. This structure continues to extend in the radial direction, leaving a web of particles around the centers. At a later time, the formation of ringlets propagate radially away from the center of collision, and then the effects of instability involved leads to a reconnection in which small-scale ringlets are generated. In addition, it is shown that the scheme captures several experimentally observed features of the ring collisions, including a turbulent breakdown into small-scale structures and the generation of small-scale radially propagating vortex rings, due to the modification of the vorticity distribution, as a result of the entrainment of background vorticity and helicity by the vortex core, and their subsequent interaction.

Vortex emission from quantum turbulence in superfluid4He

An oscillating object can stretch quantized vortices attached to it in superfluids due to the relative superflow, steadily generating quantum turbulence, even in the zero-temperature limit. We report the emission and propagation of quantized vortices from quantum turbulence generated in superfluid ${}^{4}$He at low temperatures. A vortex-free vibrating wire enables us to detect the first collision of vortex rings and therefore to measure the time-of-flight of a vortex emitted from a generator to a detector. The detection times from the start of turbulence generation exhibit an exponential distribution, suggesting that the detection is a Poisson process. Vortices are emitted continuously, but each vortex has a random flight velocity and direction. We estimated the nondetection time and mean detection period from the distribution for two flight distances. By estimating the flight velocity, we find that only vortices with velocities lower than the detector velocity can be detected, even if the sizes of the emitted vortices are smaller than the wire thickness or the vibration amplitude. The ratio of the detection rate as a function of vortex velocity suggests anisotropic emission of vortices from the quantum turbulence.

渦法による渦輪の成長過程について(G05-11 渦・噴流,G05 流体工学部門一般講演)

渦法による渦輪の成長過程について(G05-11 渦・噴流,G05 流体工学部門一般講演)

Decay of superfluid turbulence via Kelvin-wave radiation

The decay of superfluid turbulence in the limit of low temperature is studied by numerical simulations of vortex ring collisions. In particular we excite Kelvin waves and study the loss of vortex line length due to Kelvin-wave radiation. Although the effect is small, the decay constant is not inconsistent with recent experiments on vortex lattices in dilute Bose-Einstein condensates, and on superfluid turbulence in helium at very low temperature. We also consider the character of the decay when both vortex reconnections and Kelvin-wave radiation are present.

Vortex reconnection as the dissipative scattering of dipoles

We propose a phenomenological model of vortex tube reconnection at high Reynolds numbers. The basic picture is that squeezed vortex lines, formed by stretching in the region of closest approach between filaments, interact like dipoles (monopole-antimonopole pairs) of a confining electrostatic theory. The probability of dipole creation is found from a canonical ensemble spanned by foldings of the vortex tubes, with a temperature parameter estimated from the typical energy variation taking place in the reconnection process. Vortex line reshuffling by viscous diffusion is described in terms of directional transitions of the dipoles. The model is used to fit with reasonable accuracy experimental data established long ago on the symmetric collision of vortex rings. We also study along similar lines the asymmetric case, related to the reconnection of nonparallel vortex tubes.