Vortex lines and vortex tubes[edit]
A vortex line or vorticity line is a line which is everywhere tangent to the local vorticity vector. Vortex lines are defined by the relation[9]
where is the vorticity vector in Cartesian coordinates.
A vortex tube is the surface in the continuum formed by all vortex lines passing through a given (reducible) closed curve in the continuum. The 'strength' of a vortex tube (also called vortex flux)[10] is the integral of the vorticity across a cross-section of the tube, and is the same everywhere along the tube (because vorticity has zero divergence). It is a consequence of Helmholtz's theorems (or equivalently, of Kelvin's circulation theorem) that in an inviscid fluid the 'strength' of the vortex tube is also constant with time. Viscous effects introduce frictional losses and time dependence.[11]
In a three-dimensional flow, vorticity (as measured by the volume integral of the square of its magnitude) can be intensified when a vortex line is extended — a phenomenon known as vortex stretching.[12] This phenomenon occurs in the formation of a bathtub vortex in outflowing water, and the build-up of a tornado by rising air currents.
Vorticity meters[edit]
Rotating-vane vorticity meter[edit]
A rotating-vane vorticity meter was invented by Russian hydraulic engineer A. Ya. Milovich (1874–1958). In 1913 he proposed a cork with four blades attached as a device qualitatively showing the magnitude of the vertical projection of the vorticity and demonstrated a motion-picture photography of the float's motion on the water surface in a model of a river bend.[13]
Rotating-vane vorticity meters are commonly shown in educational films on continuum mechanics (famous examples include the NCFMF's "Vorticity"[14]and "Fundamental Principles of Flow" by Iowa Institute of Hydraulic Research[15]).
https://en.wikipedia.org/wiki/Vorticity#Vortex_lines_and_vortex_tubes
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