# vortex

## Definitions

• WordNet 3.6
• n vortex a powerful circular current of water (usually the result of conflicting tides)
• n vortex the shape of something rotating rapidly
• ***
Webster's Revised Unabridged Dictionary
• Vortex A mass of fluid, especially of a liquid, having a whirling or circular motion tending to form a cavity or vacuum in the center of the circle, and to draw in towards the center bodies subject to its action; the form assumed by a fluid in such motion; a whirlpool; an eddy.
• Vortex (Cartesian System) A supposed collection of particles of very subtile matter, endowed with a rapid rotary motion around an axis which was also the axis of a sun or a planet. Descartes attempted to account for the formation of the universe, and the movements of the bodies composing it, by a theory of vortices.
• Vortex (Zoöl) Any one of numerous species of small Turbellaria belonging to Vortex and allied genera. See Illustration in Appendix.
• ***
Century Dictionary and Cyclopedia
• n vortex A whirl of fluid. An intuitive geometrical idea of the motion is not easily attained. If the motion of a flnid varies continuously both in time and in space, it may be described as such that each spherical particle is at each instant receiving three compressions or elongations at right angles to one another, and has, besides, a motion of translation and a motion of rotation about an axis through it. When this motion of rotation is present, the fluid is said to have a rotational motion; but this must not be confounded with a rotation of the whole mass. Thus, if all the parts of the fluid move in one direction but with unequal velocities in different parallel planes, though there be no rotation of the whole mass, yet the motion is rotational; and if a spherical particle were suddenly congealed, its inertia would make it rotate. On the other hand, one or more radial paddles turning about the axis of a cylindrical vessel filled with a perfect fluid, though making the latter revolve as a whole, could yet impart no rotational motion, which the fluid would evade by slipping round between the paddles. The motion being perfectly continuous, the axis of rotation of a particle must join the axis of rotation of a neighboring particle, so that a curve, called a vortexline, may be described whose tangents are the axes of rotation of the particles at their points of tangency; and such a curve must evidently return into itself or reach both extremities to the boundaries of the fluid. A vortex is a portion of fluid in rotational motion inclosed in an annular surface which is a locus of vortex-lines; and an inflnitesimal vortex is called a vortex-filament. If at any part of a vortex-fllament the angular velocity is greater than at another part a little removed along the vortexline, then (considering a particle a little removed from the central vortex-line) it is plain that of two opposite parts of this particle having the same velocity in magnitude and direction and consequently on its axis of rotation, that one which is in the more rapidly moving stratum must be nearer the central vortex-line, so that the annular boundary of the vortex must present a constriction where the angular velocity is great; and thus it can be shown that the product of the meau angular velocity in any cross-section perpendicular to the vortex-lines multiplied by the area of that section is constant at all parts of the vortex. In a perfect fluid, which can sustain no distorting stress even for an instant, the velocity of a rotating particle cannot be retarded any more than if it were a frictionless sphere; and, in like manner, no such velocity can be increased. Consequently, a vortex, unlike a wave, continues to be composed of the same identical matter. When the motion is continuous throughout the fluid, two vortices exercise a singular action upon one another, each ring in turn contracting and passing through the aperture of the other, which stretches, with other singular motions.
• n vortex Any whirling or gyratory motion; also, a whirlpool.
• n vortex In the Cartesian philosophy, a collection of material particles, forming a fluid or ether, endowed with a rapid rotatory motion about an axis, and filling all space, by which Descartes accounted for the motions of the universe. This theory attracted much attention at one time, but is now entirely discredited.
• n vortex [capitalized] [NL.] In zoology, the typical genus of Vorticidæ, containing such species as V. viridis
• ***
Chambers's Twentieth Century Dictionary
• n Vortex vor′teks a whirling motion of a fluid forming a cavity in the centre: a whirlpool: an eddy having a rotational motion of the smallest visible portion in the centre
• ***

## Quotations

• Kabbalah
“The atom, being for all practical purposes the stable unit of the physical plane, is a constantly changing vortex of reactions.”
• Ezra Pound
“The Image is more than an idea. It is a vortex or cluster of fused ideas and is endowed with energy.”

## Etymology

Webster's Revised Unabridged Dictionary
L. vortex, vertex, -icis, fr. vortere, vertere, to turn. See Vertex
Chambers's Twentieth Century Dictionary
L. vortex, vertexvortĕre, vertĕre, to turn.

## Usage

### In literature:

Burke had in his vortex whirled away Windham.
"Critical and Historical Essays, Volume III (of 3)" by Thomas Babington Macaulay
The Girondists perceived distinctly the vortex of destruction toward which they were so rapidly circling.
"Madame Roland, Makers of History" by John S. C. Abbott
Descartes said the moon pressed down upon the waters by the centrifugal force of its vortex, and so produced a low tide under it.
"Pioneers of Science" by Oliver Lodge
The shells were revolving in a vortex of rushing, foaming water.
"Astounding Stories of Super-Science February 1930" by Various
What a vortex of furious horses must be there!
"Valley of Wild Horses" by Zane Grey
He must have perished in the frightful vortex of the tunnel.
"Out of the Depths" by Robert Ames Bennet
I was partly dragged, partly I went to a certain extent of my own will, into this vortex.
"The First Violin" by Jessie Fothergill
It was a variation of a vortex-stream.
"Invasion" by William Fitzgerald Jenkins
Our philosopher, now seventy years old, had come home to rest, but found himself instead in the very vortex of public affairs.
"Benjamin Franklin" by Paul Elmer More
Anyway, he plunged into a wild vortex of gambling.
"The Golden Woman" by Ridgwell Cullum
Jim was positive that he had heard her cry for help out of the vortex in the water.
"Astounding Stories of Super-Science, May, 1930" by Various
In the vortex of the eddy the delusion of the vast cone was more pronounced.
"Dwellers in the Hills" by Melville Davisson Post
Von Kettler, helpless too, was spinning round upon the opposite side of the vortex.
"Astounding Stories of Super-Science, October, 1930" by Various
Mabel Harrington, just as the vortex engulphed her.
"Mabel's Mistake" by Ann S. Stephens
She left here only to plunge into a wild vortex of experiences there.
"Liége on the Line of March" by Glenna Lindsley Bigelow
The sun is a dizzying scarlet blaze, the sky a violet vortex whirling over me.
"Shirley" by Charlotte Brontë
The same caution applies, manifestly, to all the other speculations which have the vortex atom, so to say, for their foundation-stone.
"A History of Science, Volume 5(of 5)" by Henry Smith Williams
I am prepared to say that there will be no evidences of a vortex wind in or near Empiria.
"A Republic Without a President and Other Stories" by Herbert Ward
Now Boone was in some unaccountable vortex and talking wildly of inciting men who needed to be calmed.
"The Tempering" by Charles Neville Buck
Michael during the year at Two Hundred and Two scarcely saw anybody who was not in the heart of the main athletic vortex of the university.
"Sinister Street, vol. 2" by Compton Mackenzie
***

### In poetry:

Is death so near, then?
From this blazing light,
Do I plunge suddenly
Into vortex? Night?
"The Approach" by Robert Nichols
Virtue and truth attend him,
Into the vortex whirled,
God and His angels defend him—
A boy has gone into the world.
"Into The World" by Ella Wheeler Wilcox
Oh no. To see him again —
it would not matter where —
or inside the boiling vortex,
under serene moons or in bloodless fright!
"To See Him Again" by Gabriela Mistral
And better still than these gorglorious Things
The Briar's gracious Narcotine that clings
To my ambrosial Temples till I wear
A Halo-crown of vapoured Vortex Rings.
"The Rubáiyát of Omar Khayyám Jr." by Wallace Irwin
What is secure from the land-dashing wave?
There go our riches, and our hopes fly there;
There go the faces of our best beloved,
Whelmed in the vortex of its wild despair.
"Consolation" by Harriet Beecher Stowe
Bind us in time, O Seasons clear, and awe.
O minstrel galleons of Carib fire,
Bequeath us to no earthly shore until
Is answered in the vortex of our grave
The seal's wide spindrift gaze toward paradise.
"Voyages II" by Harold Hart Crane

### In news:

Often it's a tiny slip that becomes a vortex of disaster.
Here's a big reason: This Jurassic-sized vortex that's totally dominating the central part of the country.
In September, the 49-year-old New Jersey native found himself in the vortex of a selectmen's debate over whether there is a homeless problem in Ayer.
Vortex has released the HDPV2 gate , which offers significant enhancements over the original HDP design.
If it is a vortex thank god it was horizontal and maybe too low to the ground to become vertical.
Red rocks and healing vortexes.
Proposed fines for Vortex Recycling total \$58,000.
The submission with the most votes will win the Ultimate Vortex Optics Package.
Michael O'Donnell reviews the Polycom Vortex EF2280.
The Vortex Flow Insert from IPEX USA helps eliminate odorous emissions and minimize corrosion in vertical sewer drops.
Because it fits and feels like a conventional stability shoe, the Vortex may be a shoe that can convince skeptical runners to give Spiras spring technology a try.
Vortex Spray-On Bed Liner.
Vortex Spray On Bed Liner Sharp Edge.
Vortex Spray On Bed Liner Orbital Sanders.
Bristow Expands Training With Vortex Buy.
***

### In science:

One may physically understand the form of the theory (1) as follows : the exact integration over the gauge-ﬁeld ~a, which appears only linearly in (1), leaves the spinon-vortex coupling i ~A · ~JΦ , where ∇ × ~A = π ~JΨ , and ~JΨ and ~JΦ are the spin and vortex current densities, respectively.
Theory of spin response in underdoped cuprates as strongly fluctuating d-wave superconductors
We analyze the latter case in detail and establish (analytically and numerically) the stability of the S = 2 vortex in that setting for parametric regimes similar to the ones for which the discrete vortex of S = 1 has been found to be stable.
Stabilizing the Discrete Vortex of Topological Charge S=2
The vortex density being uniform, even in presence of interactions, we consider the ﬁrst order correction in g to the vortex pair distribution function ρ2 (u).
Seeing zeros of random polynomials: quantized vortices in the ideal Bose gas
FIG. 11: Semi-log plots of the vortex chemical potential, µ, vs. the longitudinal vortex density, n, for a box disorder distribution and two values of d.
Transverse Meissner Physics of Planar Superconductors with Columnar Pins
FIG. 12: Semi-log plot of the vortex chemical potential, µ, vs. the longitudinal vortex density, n, for two displaced powerlaw distributions as in Fig. 10.
Transverse Meissner Physics of Planar Superconductors with Columnar Pins
The physical quantity in the vortex pinning problem that the parameters µ and Γµ determine is the vortex density, n.
Transverse Meissner Physics of Planar Superconductors with Columnar Pins
The chemical potential, µ, in this case is a tuning parameter that controls the vortex ﬁlling factor of the lattice, and hence the longitudinal vortex density.
Transverse Meissner Physics of Planar Superconductors with Columnar Pins
Note that the oscillations do not correspond to Tkachenko waves, since the HVBK equations assume that the free energy of the vortex array depends only on the vortex line density, not on vortex lattice deformations (Chandler & Baym 1983, 1986; Donnelly 1991).
Transitions between turbulent and laminar superfluid vorticity states in the outer core of a neutron star
We show that under these conditions, by changing the mass geometry, one can also bring one vortex manifold to any other preassigned vortex manifold.
Control of mechanical systems on Lie groups and ideal hydrodynamics
The distribution of the vortex vector ﬁelds in always integrable, thus they deﬁne a manifold, that we call the vortex manifold.
Control of mechanical systems on Lie groups and ideal hydrodynamics
We show that under these conditions, by changing the mass geometry, one can bring the whole vortex manifold to any other preassigned vortex manifold.
Control of mechanical systems on Lie groups and ideal hydrodynamics
Notice that in the inﬁnite-dimensional case, vortex ﬁelds cam still deﬁne a certain commutative subgroup, which can also be referred to as ”vortex manifold”.
Control of mechanical systems on Lie groups and ideal hydrodynamics
By Theorem 2.3, the vector ﬁelds vλ (g ) and the vortex ﬁelds w(g ) commute (the vortex ﬁelds are right-invariant, while the vectors Lg∗λi are left-invariant, and we have also assumed that u(t) is piecewise constant).
Control of mechanical systems on Lie groups and ideal hydrodynamics
The distribution of the vortex ﬁelds is always integrable, thus it deﬁnes a manifold (at least locally), that we call a vortex manifold.
Control of mechanical systems on Lie groups and ideal hydrodynamics
When many vortex lines are created a regular vortex lattice is formed and the angular momentum acquired by the system approaches the classical rigid-body value.
Theory of ultracold Fermi gases
***