VORTICITY, a beautiful fluid mechanics phenomena, but which can have devastating effects on human settlements, when of very large scale and very powerful.

The complete vortex has a “donut” shape. Fluid/wind sweeps in along a flat bottom (ground level, or sea level), increasingly curving as it converges to the central “funnel.” There, it spirals up and as it rises it also spirals outward, and the curvature of the “path lines” diminishes at further radial distances. “Out there” those pathlines (water flow, winds) cycle back down to the “bottom” plane, completing a circuit, and then flow in again.

Versions of vortices are everywhere: bathtub drains, river eddies, hurricanes, water spouts, airplane wingtip vorticies, Great Red Spot on Jupiter.

Herman Helmholtz (19th century physicist) published his conservation law of vorticity (Helmholtz Vortex Theorem), and the differential equation form of vorticity involves “the curl” (a differential vector cross product of the velocity field). Vorticity features in Boundary Layer Theory (for the thin viscous layers adhering to material bodies moving through fluid bodies, like airplane wings, and further explicated by Von Karman, in the early 20th century, about the trailing Von Karman Vortex Street behind airplane wings, a consequence of fluid viscosity).

The best (and still and forever likely to remain incomplete) theory/description of fluid turbulence is that it is a nested set of vorticies of increasing scale, from the nearly molecular up to larger and larger eddies until a macro-level of fluid mass circulation — like a tornado.

If the fluid is electrified, and consequently magnetized, like the atmospheres of the Sun and stars, Earth’s ionosphere and the Earth molten core, and so much of Space (nebulas, planetary rings, space plasmas: novas and supernovas and rarefied space dust), then electric and magnetic vortices can form: Earth’s magnetic field is one example of the outer “path lines” of Earth’s ‘magnetic tornado’ at its core.

Vorticity in its many forms is quite fascinating, but of course violent vortical weather like hurricanes and tornadoes can be so harmful to living creatures: plants and animals, including humans. The American Great Plains are a natural “Tornado Alley” because of the expanse of flatness allowing the geometry of the tornado vortex free reign to expand without restraint. Also, they form there because warm humid air from the Gulf of Mexico is propelled northward (by its contained heat energy = “high pressure”) and over the Plains it collides with strong colder winds sweeping down eastward from the Rocky Mountains (the Front Range), and that collision of low hot moist northward wind with high dry cold eastward winds creates a counterclockwise circulatory motion of atmospheric masses, with moisture rising (in the central “funnel”), chilling, raining out, freezing into ice crystals and hail, and the friction of that creating electrical charge separation (“static” electricity) which sparks over as lightning.

The point about Helmholtz’s Vortex Theorem is that the continuous threading of the “path lines” into the vortex “spool” makes of the whole an integral energetic structure, and that integrity is maintained — conserved — despite forces imposed on the whole of it: which is why hurricanes and tornadoes move, intact, across the face of the Earth because of the imposition of pressure gradients from “high pressure” regions to “low pressure” regions.

Another aspect of Helmholtz’s theorem is that, like a spinning ice skater, the slow gradual circulation out at vast distance (ice skater with arms extended, spinning slowly) represents an angular moment that is maintained close to the center by a very rapid rate of spin (ice skater with arms pulled in, spinning quickly).

So it takes quite a bit to dissipate the vortex, in fluids it is the result of the build-up of friction (fluid viscosity) gradually breaking up vortical motion into randomized turbulence (in the absence of strong external — collisional wind — forces causing a macro “stirring” into counterclockwise circulation — in the Northern Hemisphere). Stirring cream in your coffee is a nice way to observe vortical motion and vortical mixing.

Back in the 1980s I had a lot of fun working out a theory of electromagnetic vortices (all based on the work of famous physicists, like Debye, Alfvén, Cowling, and their MHD and plasma physics predecessors), which I found were produced by nuclear explosions in magnetized spaces, and in very high current and high power electrical transmission lines as used for fusion power and particle beam research.

If you have a poetic inclination toward reading about vortices, look into the book ‘Sensitive Chaos’ by Theodor Schwenk, an anthroposophist — influenced by Rudolf Steiner — about the many intriguing patterns in fluid flows of all kinds (as in our blood streams, the swirled forms of some of our blood vessel junctions and valves).

Nature is endlessly fascinating and instructive.



Space & Time Dependent Boltzmann Distribution of Electrons in Gases

(28 June 1994, and a bit later)

Analytical Time Dependent Boltzmann Distribution of Electrons in Gases with Inelastic Collisions
Boltzmann Electrons (t)

Analytical Space and Time Dependent Boltzmann Distribution of Electrons in Gases with Inelastic Collisions
Boltzmann Electrons (x,t)

PDF files of the two reports are available from the links above; the reports are displayed below.



Electric Vortex in MHD Flow

(Spring 1995)

Electric Vortex in MHD Flow

A PDF file of this report is available from the link above; and the report is displayed below.


Closely related:

Proton Beam Driven Electron MHD


DC Planar Magnetron Cathode 2D Fluid Model


Related post:



Proton Beam Driven Electron MHD

MHD 1984
[“MHD 1984” is a link to a PDF file of the following.]


Addendum, 7 March 2018

Alfvén’s magnetic pumping (by hydromagnetic or Alfvén waves), and hydromagnetic shocks are now recognized by computational physical science.

Scientists crack 70-year-old mystery of how magnetic waves heat the sun
March 6, 2018, Queen’s University Belfast


In 1942, Swedish physicist and engineer Hannes Alfvén presented his theory of hydromagnetic waves, for which he won the Nobel Prize in physics in 1970. Between 1983 and 1985, I tried to convince my supposed colleagues and science-bureaucrat superiors (timorous bosses and climbers at Livermore, and also Los Alamos) to study this type of magnetic wave phenomenon, after I found ample evidence of it in very elaborate computer simulations of nuclear explosions (simulations of which was all they knew how to do) driving moderately relativistic magnetohydrodynamics (which they did not recognize nor understand at all). So, I enjoyed reading about the new advances in hydromagnetic wave physics made by the Queen’s University Belfast. My cartoon physics monograph on the subject (to the extent I could understand it), from 1983-1985, is available at my blog under the title “Proton Beam Driven Electron MHD.” One of my favorite works ever.