Instability and reconnection in the head-on collision of two vortex rings

Lim, T. T.; Nickels, T. B.

doi:10.1038/357225a0

Cited by 128 publications

(133 citation statements)

References 7 publications

Supporting

Mentioning

108

Contrasting

Unclassified

Order By: Relevance

“…The alternating signs of the outer regions indicate the production of smaller rings of opposite polarity, thus ensuring P ¼ 0 throughout the process. The generation and shoot-off of smaller rings from the plane of collision in opposite directions seems in agreement with the experimental results of Lim and Nickels [17].…”

Section: Multi-component Systems: Vortex Linkssupporting

confidence: 80%

See 1 more Smart Citation

Structural Complexity of Vortex Flows by Diagram Analysis and Knot Polynomials

Ricca

2013

How Nature Works

View full text Add to dashboard Cite

In this paper I present and discuss with examples new techniques based on the use of geometric and topological information to quantify dynamical information and determine new relationships between structural complexity and dynamical properties of vortex flows. New means to determine linear and angular momenta from standard diagram analysis of vortex tangles are provided, and the Jones polynomial, derived from the skein relations of knot theory is introduced as a new knot invariant of topological fluid mechanics. For illustration several explicit computations are carried out for elementary vortex configurations. These new techniques are discussed in the context of ideal fluid flows, but they can be equally applied in the case of dissipative systems, where vortex topology is no longer conserved. In this case, a direct implementation of adaptive methods in a real-time diagnostics of real vortex dynamics may offer a new, powerful tool to analyze energy-complexity relations and estimate energy transfers in highly turbulent flows. These methods have general validity, and they can be used in many systems that display a similar degree of self-organization and adaptivity.

show abstract

Section: Multi-component Systems: Vortex Linkssupporting

confidence: 80%

“…7). This process has been actually realized by head-on collision of coloured vortex rings in water by Lim & Nickels [17]. Since at the initial state linear momentum P ¼ 0 (for symmetry reason), we expect that this remains so, till reconnections take place.…”

Section: Multi-component Systems: Vortex Linksmentioning

confidence: 99%

Structural Complexity of Vortex Flows by Diagram Analysis and Knot Polynomials

Ricca

2013

How Nature Works

View full text Add to dashboard Cite

show abstract

“…At low Reynolds numbers, reconnection occurs in a seemingly simple (laminar) way [35][36][37][38][39]. The process can be described by an elegant model [40], which very successfully reproduces the main features observed in low-resolution numerical studies [41].…”

Section: Discussionmentioning

confidence: 75%

Potential singularity mechanism for the Euler equations

2016

View full text Add to dashboard Cite

Singular solutions to the Euler equations could provide essential insight into the formation of very small scales in highly turbulent flows. Previous attempts to find singular flow structures have proven inconclusive. We reconsider the problem of interacting vortex tubes, for which it has long been observed that the flattening of the vortices inhibits sustained self-amplification of velocity gradients. Here we consider an iterative mechanism, based on the transformation of vortex filaments into sheets and their subsequent instability back into filaments. Elementary fluid mechanical arguments are provided to support the formation of a singular structure via this iterated mechanism, which we analyze based on a simplified model of filament interactions.

show abstract

“…This scenario is observed in the experiment of the head-on collision of two vortex rings (e.g. Lim & Nickels 1993), in which the role of the dye is analogous to the vortex-surface scalar field used in the present study to identify the vortical structures in the Lagrangian sense. …”

Section: 3mentioning

confidence: 84%

On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions

Yang

Pullin

2010

J. Fluid Mech.

View full text Add to dashboard Cite

For a strictly inviscid barotropic flow with conservative body forces, the Helmholtz vorticity theorem shows that material or Lagrangian surfaces which are vortex surfaces at time t = 0 remain so for t > 0. In this study, a systematic methodology is developed for constructing smooth scalar fields φ(x, y, z, t = 0) for Taylor-Green and KidaPelz velocity fields, which, at t = 0, satisfy ω · ∇φ = 0. We refer to such fields as vortex-surface fields. Then, for some constant C, iso-surfaces φ = C define vortex surfaces. It is shown that, given the vorticity, our definition of a vortex-surface field admits non-uniqueness, and this is presently resolved numerically using an optimization approach. Additionally, relations between vortex-surface fields and the classical Clebsch representation are discussed for flows with zero helicity. Equations describing the evolution of vortex-surface fields are then obtained for both inviscid and viscous incompressible flows. Both uniqueness and the distinction separating the evolution of vortex-surface fields and Lagrangian fields are discussed. By tracking φ as a Lagrangian field in slightly viscous flows, we show that the well-defined evolution of Lagrangian surfaces that are initially vortex surfaces can be a good approximation to vortex surfaces at later times prior to vortex reconnection. In the evolution of such Lagrangian fields, we observe that initially blob-like vortex surfaces are progressively stretched to sheet-like shapes so that neighbouring portions approach each other, with subsequent rolling up of structures near the interface, which reveals more information on dynamics than the iso-surfaces of vorticity magnitude. The non-local geometry in the evolution is quantified by two differential geometry properties. Rolled-up local shapes are found in the Lagrangian structures that were initially vortex surfaces close to the time of vortex reconnection. It is hypothesized that this is related to the formation of the very high vorticity regions.

show abstract

Instability and reconnection in the head-on collision of two vortex rings

Cited by 128 publications

References 7 publications

Structural Complexity of Vortex Flows by Diagram Analysis and Knot Polynomials

Structural Complexity of Vortex Flows by Diagram Analysis and Knot Polynomials

Potential singularity mechanism for the Euler equations

On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions

Contact Info

Product

Resources

About