Complete measurement of helicity and its dynamics in vortex tubes

@article{Scheeler2017CompleteMO,
  title={Complete measurement of helicity and its dynamics in vortex tubes},
  author={Martin W Scheeler and Wim M. van Rees and Hridesh Kedia and Dustin Kleckner and William T. M. Irvine},
  journal={Science},
  year={2017},
  volume={357},
  pages={487 - 491}
}
Linking fluids as they twist and writhe Helicity is a measure of cork-screw-like motion described by the amount of twisting, writhing, and linking in a fluid. Total helicity is conserved for ideal fluids, but how helicity changes in real fluids with even tiny amounts of viscosity has been an open question. Scheeler et al. provide a complete measurement of total helicity in a real fluid by using a set of hydrofoils to track linking, twisting, and writhing (see the Perspective by Moffatt). They… Expand
Helicity—invariant even in a viscous fluid
TLDR
On page 487 of this issue, Scheeler et al. (3) explore a particular property of a vortex ring whose core is helical rather than circular in form, an integral over the fluid domain that expresses the correlation between velocity and vorticity. Expand
Construction of knotted vortex tubes with the writhe-dependent helicity
We propose a feasible method for constructing knotted vortex tubes with the finite thickness and arbitrary complexity and develop an accurate algorithm to implement this method in numericalExpand
Helicity spectra and topological dynamics of vortex links at high Reynolds numbers
Abstract We employ reconnection-capable, vortex filament methods and finite-volume, Navier–Stokes flow solvers to investigate the topological and helicity dynamics of vortex links for medium and highExpand
Classical helicity of superfluid helium
Helicity - a quadratic invariant of the classical Euler equation like the energy - plays a fundamental role in turbulent flows, controlling the strength of the nonlinear interactions which cascadeExpand
Helicity in superfluids: Existence and the classical limit
In addition to mass, energy, and momentum, classical dissipationless flows conserve helicity, a measure of the topology of the flow. Helicity has far-reaching consequences for classical flows fromExpand
Topological constraints in the reconnection of vortex braids
We study the relaxation of a topologically non-trivial vortex braid with zero net helicity in a barotropic fluid. The aim is to investigate the extent to which the topology of the vorticity field --Expand
M ay 2 01 8 Classical helicity of superfluid helium
Helicity a quadratic invariant of the classical Euler equation like the energy plays a fundamental role in turbulent flows, controlling the strength of the nonlinear interactions which cascade energyExpand
Reconnection of vortex tubes with axial flow
This paper addresses the interaction of initially anti-parallel vortex tubes containing an axial flow that induces a twisting of the vortex lines around the tube axes, using numerical simulations.Expand
Effects of twist on the evolution of knotted magnetic flux tubes
We develop a general method for constructing knotted flux tubes with finite thickness, arbitrary shape and tunable twist. The central axis of the knotted tube is specified by a smooth andExpand
Topological mechanics of knots and tangles
TLDR
The authors show why some common knots slip easily and untie, whereas others hold tight, and highlight the importance of twist and writhe in unknotting processes, providing guidance for the control of systems with complex entanglements. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 63 REFERENCES
Helicity conservation by flow across scales in reconnecting vortex links and knots
TLDR
The reassociation of vortex lines through a reconnection enables the transfer of helicity from links and knots to helical coils, and a new method for quantifying the spatial helicity spectrum is found that the reconnection process can be viewed as transferring helicity between scales, rather than dissipating it. Expand
Velocity, energy, and helicity of vortex knots and unknots.
TLDR
The velocity, the energy, and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (as toroidal and poloidal coils) in a perfect fluid are determined. Expand
Helicity and singular structures in fluid dynamics
  • H. K. Moffatt
  • Physics, Medicine
  • Proceedings of the National Academy of Sciences
  • 2014
TLDR
Issues of the dynamics of fluids that are of central importance for (i) the origin of planetary and astrophysical magnetism, and (ii) the determination of stable magnetic field configurations used in thermonuclear fusion reactors like the tokamak are covered. Expand
Conservation of writhe helicity under anti-parallel reconnection
TLDR
It is shown that the writhe is conserved under anti-parallel reconnection, which means that any deviation from helicity conservation is entirely due to the intrinsic twist inserted or deleted locally at the reconnection site. Expand
Helicity and the Călugăreanu invariant
  • H. K. Moffatt, R. L. Ricca
  • Mathematics
  • Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
  • 1992
The helicity of a localized solenoidal vector field (i.e. the integrated scalar product of the field and its vector potential) is known to be a conserved quantity under ‘frozen field’ distortion ofExpand
The topological properties of magnetic helicity
The relation of magnetic helicity to the topological structure of field lines is discussed. If space is divided into a collection of flux tubes, magnetic helicity arises from internal structureExpand
The degree of knottedness of tangled vortex lines
Let u(x) be the velocity field in a fluid of infinite extent due to a vorticity distribution w(x) which is zero except in two closed vortex filaments of strengths K1, K2. It is first shown that theExpand
Linking of vortex rings
THE topology of vortex lines, which trace the local vorticity in a fluid flow just as streamlines trace the velocity, is important in attempts to understand, describe and control flows in variousExpand
The energy and helicity of knotted magnetic flux tubes
  • A. Chui, H. K. Moffatt
  • Mathematics
  • Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
  • 1995
Magnetic relaxation of a magnetic field embedded in a perfectly conducting incompressible fluid to minimum energy magnetostatic equilibrium states is considered. It is supposed that the magneticExpand
Stretched vortices - the sinews of turbulence; large-Reynolds-number asymptotics
A large-Reynolds-number asymptotic theory is presented for the problem of a vortex tube of finite circulation r subjected to uniform non-axisymmetric irrotational strain, and aligned along an axis ofExpand
...
1
2
3
4
5
...