International Encyclopedia of Systems and Cybernetics

A flow rotating about an axis within some medium which acts as an environment.

Vortices may appear in the most different types of fluids: stars clustered in spiral galaxies, planetary atmospheres (cyclones, hurricanes, typhons), oceanic waters, glaciers, rivers, vegetal and animal tissues, etc…

The French engineer Ch. LAVILLE devoted a book to vortices and wrote: "Whirling flows are trajectories along lines of least resistance. This implies that they condition the duration possibilities of a phenomenon".

"Vortices appear as phenomena limited in time and space: they arise, they grow, they go through a period of dynamic stability, they decline and disappear". Even so, they may frequently remain dynamically stable for a long duration.

"The emergence of a vortex is submitted to two conditions: an adequate environment, fluid by necessity (gazeous, liquid or finely divided solid) and a certain heterogeneity in this environment. In fact, all vortices arise from a movement of tangential opposition upon a mass in translation, thus creating a gyratory movement. Vortices thus result of the conjugated action of the central force that produced the translation and a couple creating the gyration; in other words, they are determined by a dissymmetry and, in their initial phase, they appear as a coil in the fluid mass"…

"The composition of both movements, translation and gyration, that characterizes the vortex, produces closed helicoidal lines developing around a central axis, thus materializing brachystochrone (i.e. of shortest duration in time) trajectories"…

"The vortex, in synthesis becomes individualized within the amorphous mass, of which it separated to take its form. To reach to this shape, it conforms to the following condition: The structural set of its current or tension lines communicates it resistance to oppose its deformation or destructuration by the environment" (1950, p.52-54).

These characteristics clearly show that all complex systems are in a sense stationary vortices of structuring energy.

The vortex model is quite important for the understanding of the genesis of systems. It relates to the following complex phenomena:

- the basic symmetry-breakings

- the resulting instabilities of energy flows

- the energy-matter equivalence

- the process-structure interrelations

- the genesis and transformation of forms

See for instance d'ARCY WENTWORTH THOMPSON book "On growth and form"(1916).

LAVILLE made moreover these interesting comments:

- Vortices are minimum resistence trajectories and, consequently condition the possibility of duration of a phenomenon.

- Vortices as phenomena are limited in space and time: they arise, grow, attain dynamic stability for some time, until they decline and disappear.

- A vortex separates from its environment and acquires an identity

- As its field communicates it a resistence to external disturbance, it becomes a more or less durable organization. (Ibid)

This last point offers an interesting insight into the very basic and general nature of autopoiesis and organizational closure models.

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