A rotational form of fluid flow. Lines of flow are curved, and may even form closed loops. Examples of vortices are whirlpools, tornadoes, and the circulating eddies caused by obstructions in rivers.
A vortex (pl. The shape of media or mass rotating rapidly around a center forms a vortex.
Dynamics
A vortex can be any circular or rotary flow that possesses vorticity. Vorticity is a mathematical concept used in fluid dynamics. It can be related to the amount of "circulation" or "rotation" in a fluid. In fluid dynamics, vorticity is the circulation per unit area at a point in the flow field. Also in fluid dynamics, the movement of a fluid can be said to be vortical if the fluid moves around in a circle, or in a helix, or if it tends to spin around some axis. In the atmospheric sciences, vorticity is a property that characterizes large-scale rotation of air masses. Since the atmospheric circulation is nearly horizontal, the (3 dimensional) vorticity is nearly vertical, and it is common to use the vertical component as a scalar vorticity.
Mathematically, it is defined as,
where u = ui + vj + wk is the fluid velocity.
The properties of vorticity in 2 and 3 dimensions are treated in some depth in George Batchelor's famous textbook (ch 5 &
Two types of vortex
In fluid mechanics, a distinction is often made between two limiting vortex cases. One is called the free (irrotational) vortex, and the other is the forced (rotational) vortex. These are considered as below:
top: two autumn leaves in an irrotational vortex preserve their original orientation while moving counter-clockwise.Free (irrotational) vortex
When fluid is drawn down a plug-hole, one can observe the phenomenon of a free vortex.
The tangential velocity is given by:
(2.1)where Γ is the circulation and r is the radial distance from the center of the vortex.
In non technical lingo, the circular streamlines toward the center can sweep out a given angle faster than the outer streamlines. The speed along the circular path of flow is held constant or decreases as you move out from the center. Imagine a leaf floating in a free vortex. The outer flow is slow in terms of angle traversed and it exerts a backwards tug on the base of the leaf while the faster inner flow pulls the tip forwards.
Forced (Rotational) Vortex
In a forced vortex the fluid essentially rotates as a solid body (there is no shear). The motion can be realised by placing a dish of fluid on a turntable rotating at T radians/sec; the fluid has vorticity of 2 T everywhere, and the free surface (if present) is a parabola.
The tangential velocity is given by:
(2.2)where ω is the angular velocity and r is the radial distance from the center of the vortex.
Observations
A vortex can be seen in the spiraling motion of air or liquid around a center of rotation. Circular current of water of conflicting tides form vortex shapes. A good example of a vortex is the atmospheric phenomenon of a whirlwind or a tornado or dust devil.
A mesovortex is on the scale of a few miles (smaller than a hurricane but larger than a tornado). [2] On a much smaller scale, a vortex is usually formed as water goes down a drain, as in a sink or a toilet. This whirlpool is caused by water flowing out of a small opening in the bottom of a basin or reservoir. This swirling flow structure within a region of fluid flow opens downward from the water surface.
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