From Bob Clark (931214.1650 EST)

Martin Taylor (931208 18:30):

It certainly IS dissipative, but a sustained vortex, such as one
seen when water goes down a drain at the same rate as water is
supplied upstream, does not vanish. It is a stable structure, at
least it maintains its structure against mild disturbances. It is
not at all like the case of a ball-in-a-bowl, in which a disturbance
supplies energy to the ball, to be released (into heat) when the
ball drops down to its previous position.

The "sustained vortex when water goes down a drain" to which you
refer, is a well-known phenomenon in physics. It involves the
"Coriolis Force" and is usually discussed in terms of conservation of
angular momentum. The energy to replace the frictional and viscous
losses may come either from the inflow you mention, or simply from
the decrease in gravitational energy as the water moves closer to the
center of the earth. It works just as well when the drain is
connected to a stationary bowl of water. More completely: The
surface of the earth (and the bowl of water) is moving rather rapidly
(perhaps 1000 miles per hour at my latitude). Thus, the water has a
significant amount of angular momentum. The radius of the water,
with respect to the center of the earth, decreases as the water moves
toward the center of the earth. The resulting reduction in angular
momentum is compensated by an increase of angular momentum of the
water rotating in the pipe. A complete analysis is a bit more
complicated, but includes the interesting conclusion that rotation in
the Northern Hemisphere is opposite that in the Southern Hemisphere.
These opposite rotations are observed.

The same considerations are also involved in the formation of
tornadoes and some other weather phenomena.

From the standpoint of energy and momentum, these are exactly the

same as the ball-in-a-bowl.

In the preceding paragraphs, the earth is taken as the physical
reference system. This is arbitrary, for mathematical convenience.
It both rotates about its axis and exerts gravitational force with
respect to its center. This phrase, "reference system" is entirely
different from, "reference level" in PCT.

Bill Powers (931209.0600 MST) suggests:

I think a vortex is probably much like a marble in a bowl. To
disturb a vortex you must either add or subtract some angular
momentum from it, which moves it away from its equilibrium state of
minimum potential energy.

A vortex, as such, has no particular potential energy. In this
respect it differs from the "marble & bowl." It does have kinetic
energy -- of rotation. And that energy is retained until it is
frittered away by effects of friction and viscosity (which also
involves friction). Perhaps a spinning top would be more appropriate
than a "marble & bowl."

Bill concludes:

But the forces are what cause the vortex to work.

Not quite. Better: "forces are what establish and maintain the
vortex." It continues until overcome by frictional forces that
dissipate the kinetic (rotational) energy. The forces involved can
be calculated from a suitable extension of Newton's Laws to
rotational motion. The resulting relationships are more easily
conceived in terms of conservation of momentum than interaction of

I hope this clarifies some of these ideas.

Regards, Bob Clark

I hope this clarifies some of these ideas.

Almost: Do vortices involve negative feedback? Are vortices control
systems? Is their stability the result of attraction or control?


Cliff Joslyn, Cybernetician at Large, 327 Spring St #2 Portland ME 04102 USA
Systems Science, SUNY Binghamton NASA Goddard Space Flight Center
cjoslyn@bingsuns.cc.binghamton.edu joslyn@kong.gsfc.nasa.gov

V All the world is biscuit shaped. . .