vortex

1. A spiral motion of fluid within a limited area, especially a whirling mass of water or air that sucks everything near it toward its center.
2. A place or situation regarded as drawing into its center all that surrounds it: "As happened with so many theater actors, he was swept up in the vortex of Hollywood" (New York Times).

[Latin vortex, vortic-, variant of vertex, from vertere, to turn.]

In common usage, a fluid motion dominated by rotation about an isolated curved line in space, as in a tornado, a whirlpool, a hurricane, or a similar natural phenomenon. The importance of vortices is due to two characteristics: general fluid flows can be represented by a superposition of vortices; and vortices, once created, have a persistence that increases as the effects of viscosity are reduced. The aerodynamic lift forces and most other contributors to the forces and moments on aircraft and other bodies moving through fluids do not exist in the absence of vortices. See also Aerodynamic force; Hurricane; Tornado; Waterspout.

The strength of rotation is measured by a vector called the vorticity, ω, defined as the curl of the velocity vector. A region of flow devoid of vorticity is known as irrotational. The spatial distribution of the vorticity vector provides a precise characterization of the rotation effects in fluids, and the nature of what subjectively and popularly would be called a vortex. See also Calculus of vectors; Laplace's irrotational motion.

The vorticity vector field can be constructed by measuring the instantaneous angular velocity of small masses of fluid. The vorticity vector is twice the local angular velocity vector. Starting at any arbitrary point in the fluid, a line, called a vortex line, can be drawn everywhere parallel to the vorticity vector.

A bundle of vortex lines defines a tubular region of space, called a vortex tube, with a boundary surface that no vortex line crosses.

Two simple rules follow from the definitions: (1) a vortex tube must either close on itself or end on a boundary of the fluid (including extending to “infinity” if the fluid is imagined to fill all space); and (2) at every cross section of a given vortex tube, the area integral of the normal vorticity has the same value at any given instant. The area integral is, by Stokes' theorem, equal to a line integral around the periphery of the tube, namely, the line integral of the velocity component parallel to the direction of the line integral. This quantity is also known as the circulation around the line, so at an instant of time a vortex tube has a unique value of the circulation applying to all cross sections (see illustration).

Vortex tube; ω is the vorticity.

Vortex lines confined to a layer rather than a tube describe fluid motion of a different character. This is most easily visualized when the direction of the vorticity does not vary, so all of the vortex lines are straight and parallel. Assuming the vorticity has zero magnitude outside the layer, this vortex layer represents a flow with a different speed and direction on either side of the layer. Such a change in speed occurs at the edge of wakes produced by wind passing over an obstacle. Reducing the thickness of this layer of vorticity to zero leads to an idealization known as a vortex sheet, a surface in space across which there is a finite jump in velocity tangent to the surface. Vortex sheets have a tendency to roll up, because of self-induction.

Pl. vortices [L.] a whorled or spiral arrangement or pattern, as of muscle fibers, or of the ridges or hairs of the skin.

• v. cordis — the spiral pattern of the loops of muscle fibers at the apex of the heart.
• v. pilorum — the meeting place of hair streams to form whorls.

Dansk (Danish)
n. - hvirvel, malstrøm

Nederlands (Dutch)
maalstroom, draaikolk

Français (French)
n. - (lit, fig) tourbillon

Deutsch (German)
n. - Strudel, Wirbel

Ελληνική (Greek)
n. - δίνη, στρόβιλος

Italiano (Italian)
vortice

Português (Portuguese)
n. - vórtice (m)

Русский (Russian)
вихрь, водоворот

Español (Spanish)
n. - vórtice, torbellino

Svenska (Swedish)
n. - virvel

中文（简体）(Chinese (Simplified))
旋涡, 涡流, 旋风

中文（繁體）(Chinese (Traditional))
n. - 旋渦, 渦流, 旋風

한국어 (Korean)
n. - 소용돌이, 회오리바람, 나선형 꼴

日本語 (Japanese)
n. - 渦, 渦巻き, 旋風

العربيه (Arabic)
‏(الاسم) دوارة ماء‏

עברית (Hebrew)
n. - ‮מערבולת, מערכת, עיסוק או מצב הנחשבים לבולעים לתוכם את הנמצאים בהם‬

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