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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 Aerodynamic force
The strength of rotation is measured by a vector called the vorticity, &ohgr;, 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 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 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.
ii. As used in aerodynamics, circular patterns of air created by the movement of an airfoil through the air when generating lift. As an airfoil moves through the atmosphere in sustained flight, an area of low pressure is created above it. The air flowing from the high-pressure area to the low-pressure area around and about the tips of the airfoil tends to roll up into two rapidly rotating vortices, cylindrical in shape. These vortices are the most predominant parts of aircraft wake turbulence, and their rotational force is dependent upon the wing loading, gross weight, and speed of the generating aircraft. The most important factor is weight. The greatest vortex strength occurs when the generating aircraft is heavy, clean, and slow. This situation occurs soon after a takeoff. Peak vortex tangential speeds of 300 ft/s have been recorded. A vortex can induce roll and, in rare cases, cause structural damage to the aircraft that is following the aircraft generating the vortex. The vortices from medium and heavy aircraft can be extremely hazardous to smaller aircraft, especially during takeoff and landing behind the larger aircraft.