Vortex

: vortices or vortexes)[1][2] is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved.

[3][4] Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil.

In the absence of external forces, viscous friction within the fluid tends to organise the flow into a collection of irrotational vortices, possibly superimposed to larger-scale flows, including larger-scale vortices.

Once formed, vortices can move, stretch, twist, and interact in complex ways.

A moving vortex carries some angular and linear momentum, energy, and mass, with it.

Vortices form from stirred fluids: they might be observed in smoke rings, whirlpools, in the wake of a boat or the winds around a tornado or dust devil.

When they are created, vortices can move, stretch, twist and interact in complicated ways.

Mathematically, the vorticity is defined as the curl (or rotational) of the velocity field of the fluid, usually denoted by

must not be confused with the angular velocity vector of that portion of the fluid with respect to the external environment or to any fixed axis.

may be opposite to the mean angular velocity vector of the fluid relative to the vortex's axis.

In theory, the speed u of the particles (and, therefore, the vorticity) in a vortex may vary with the distance r from the axis in many ways.

There are two important special cases, however: In the absence of external forces, a vortex usually evolves fairly quickly toward the irrotational flow pattern[citation needed], where the flow velocity u is inversely proportional to the distance r. Irrotational vortices are also called free vortices.

The ideal irrotational vortex flow in free space is not physically realizable, since it would imply that the particle speed (and hence the force needed to keep particles in their circular paths) would grow without bound as one approaches the vortex axis.

Indeed, in real vortices there is always a core region surrounding the axis where the particle velocity stops increasing and then decreases to zero as r goes to zero.

Vortex structures are defined by their vorticity, the local rotation rate of fluid particles.

A unique example of severe geometric changes is at the trailing edge of a bluff body where the fluid flow deceleration, and therefore boundary layer and vortex formation, is located.

Another form of vortex formation on a boundary is when fluid flows perpendicularly into a wall and creates a splash effect.

The velocity streamlines are immediately deflected and decelerated so that the boundary layer separates and forms a toroidal vortex ring.

A whirlpool is an example of the latter, namely a vortex in a body of water whose axis ends at the free surface.

When vortices are made visible by smoke or ink trails, they may seem to have spiral pathlines or streamlines.

In a rigid-body vortex flow of a fluid with constant density, the dynamic pressure is proportional to the square of the distance r from the axis.

In a constant gravity field, the free surface of the liquid, if present, is a concave paraboloid.

The free surface (if present) dips sharply near the axis line, with depth inversely proportional to r2.

The shape formed by the free surface is called a hyperboloid, or "Gabriel's Horn" (by Evangelista Torricelli).

A vortex that ends at the free surface of a body of water (like the whirlpool that often forms over a bathtub drain) may draw a column of air down the core.

In a moving vortex, the particle paths are not closed, but are open, loopy curves like helices and cycloids.

As long as the effects of viscosity and diffusion are negligible, the fluid in a moving vortex is carried along with it.

For example, an airplane wing that is developing lift will create a sheet of small vortices at its trailing edge.

These small vortices merge to form a single wingtip vortex, less than one wing chord downstream of that edge.

However, real fluids exhibit viscosity and this dissipates energy very slowly from the core of the vortex.