Journal ArticleDOI
The degree of knottedness of tangled vortex lines
TLDR
In this paper, the integral integral of 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 was shown.Abstract:
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 the integral
\[
I=\int{\bf u}.{\boldmath \omega}\,dV
\]
is equal to αK1K2 where α is an integer representing the degree of linkage of the two filaments; α = 0 if they are unlinked, ± 1 if they are singly linked. The invariance of I for a continuous localized vorticity distribution is then established for barotropic inviscid flow under conservative body forces. The result is interpreted in terms of the conservation of linkages of vortex lines which move with the fluid.Some examples of steady flows for which I ± 0 are briefly described; in particular, attention is drawn to a family of spherical vortices with swirl (which is closely analogous to a known family of solutions of the equations of magnetostatics); the vortex lines of these flows are both knotted and linked.Two related magnetohydrodynamic invariants discovered by Woltjer (1958a, b) are discussed in ±5.read more
Citations
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Topological methods in hydrodynamics
Vladimir I. Arnold,Boris Khesin +1 more
TL;DR: A group theoretical approach to hydrodynamics is proposed in this article, where the authors consider the hydrodynamic geometry of diffeomorphism groups and the principle of least action implies that the motion of a fluid is described by geodesics on the group in the right-invariant Riemannian metric given by the kinetic energy.
Journal ArticleDOI
The topological properties of magnetic helicity
TL;DR: The relation of magnetic helicity to the topological structure of field lines is discussed in this article, where a topologically meaningful and gauge-invariant relative measure of helicity for such volumes is presented.
Journal ArticleDOI
Flux vortices and transport currents in type II superconductors
A. M. Campbell,J. E. Evetts +1 more
TL;DR: In this paper, the authors considered the effects of lattice rigidity on the summation of pinning forces and showed that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument.
Journal ArticleDOI
Coherent structures and turbulence.
TL;DR: In this article, a general scheme for educing coherent structures in any transitional or fully turbulent flow is presented, based on smoothed vorticity maps in convenient flow planes, which recognizes patterns of the same mode and parameter size, and then phase-aligns and ensembles them to obtain coherent structure measures.
Journal ArticleDOI
Two-dimensional turbulence
Robert H. Kraichnan,D Montgomery +1 more
TL;DR: The theory of two-dimensional turbulence is reviewed and unified, and some hydrodynamic and plasma applications are considered in this paper, where some equations of incompressible hydrodynamics, absolute statistical equilibrium, spectral transport of energy and enstrophy, turbulence on the surface of a rotating sphere, turbulent diffusion, MHD turbulence, and two dimensional superflow are discussed.
References
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An Introduction to Fluid Dynamics
TL;DR: The dynamique des : fluides Reference Record created on 2005-11-18 is updated on 2016-08-08 and shows improvements in the quality of the data over the past decade.
Journal ArticleDOI
An Introduction to Fluid Dynamics. By G. K. Batchelor. Pp. 615. 75s. (Cambridge.)
TL;DR: In this paper, the Navier-Stokes equation is derived for an inviscid fluid, and a finite difference method is proposed to solve the Euler's equations for a fluid flow in 3D space.
Journal ArticleDOI
An Introduction to Fluid Dynamics.
TL;DR: In this paper, dynamique des : fluides reference record created on 2005-11-18, modified on 2016-08-08 was used for dynamique de fluides Reference Record.
Book
Introduction to Knot Theory
Richard H. Crowell,Ralph H. Fox +1 more
TL;DR: In this article, the authors define knots and knots polynomials, and present the notion of a knot polynomial and a group of knots, and prove the van Kampen theorem.