“A Taoist story tells
of an old man who accidentally fell into the river rapids leading
to a high and dangerous waterfall. Onlookers feared for his life.
Miraculously, he came out alive and unharmed downstream at the bottom
of the falls. People asked him how he managed to survive. "I
accommodated myself to the water, not the water to me. Without
thinking, I allowed myself to be shaped by it. Plunging into the
swirl, I came out with the swirl. This is how I survived."
Alan Watts
Vortex—even the word induces vertigo, sucking
us in with the archetypal power of a form that is also a function.
The function is to reduce a gradient. Nature's abhorrence of a gradient
extends beyond the temperature gradients of classical thermodynamics
to pressure gradients in fluids. Here, simple physical systems jump
to new, metastably cycling states. So-called Taylor vortices form
from the flux, spinning at birth in different directions; they multiply
in pairs with increases in the steepness of the pressure gradient
that gives rise to them; and they show a kind of history or memory.
Forty years elapsed before Bénard convection was described by mathematics.
By contrast, English physicist G. I. Taylor took a mere three years to solve
major theoretical and experimental problems associated with patterns appearing
in fluids between two rotating cylinders where a rotational pressure gradient
is set up in the fluid between the cylinders. Taylor analyzed Rayleigh's stability
criterion for rotating fluids. He predicted, in 1923, the conditions under
which fluid vortices would pop into existence. Taylor conceived a set of ingenious
experiments that used pressure gradients to produce complex flow systems. Whereas
the highly organized complex Bénard cells are driven by temperature
gradients, here pressure gradients are the subject of interest. Taylor (1923)
built a simple but precise apparatus that consisted of two cylinders, of
different diameters; the smaller one was placed inside the larger and the
space between them was filled with a fluid. Both the outer and inner cylinder
were attached to a rotary motor, an arrangement that allowed Taylor to spin
either cylinder at various speeds around the sandwiched fluid. Because of
the rotation of the fluid between the cylinders, centrifugal forces build
up, producing a pressure gradient across the fluid. From this pressure gradient,
as we will see, amazingly complex systems emerge and develop.
Each of the eight flow patterns displayed between twenty-two and thirty
pairs of vortices. At any one time only a single fluid pattern of vortices
existed. Nature, it seemed, engaged multiple ways of solving a given
problem.
In Coles's and Taylor's work nature displays
no intrinsic preference for one rather than another gradient-breaking
solution. Just as a mathematical problem can be solved in more
than one way, or a destination reached by more than a single route, inanimate
equilibrium-seeking systems can be complex and cyclical, but different.
No thermodynamic equivalent of a single correct answer on a standardized
test exists. The peculiarities of nonequilibrium systems—their intricacy and memory, the number
of cycles they incorporate, and their complexity—depend on
their particular past. In their cyclicity they embody past modes
of reaching equilibrium.
Here we see that the emergence of whirling energy-dependent systems,
their path-dependent growth and history, and even a sort of reproduction
to make use of increased energy flux, are not just properties of
life. No chemical reactions, DNA, genes, or known language are present
in these constrained fluids. Yet they show complexity, the sort of
gradient-based intricacy that in its chemical form was required for
genetics and the origins of life.
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Part
II: The Complex
8. Swirl World
9. Physics' Own "Organisms"
10. Whirlpools and Weather
Taylor flow
A, Spiral Taylor flow between
a rotating inner cylinder and a resting outer cylinder. Taylor vortices
are produced in an apparatus that consists of two cylinders, one inside
the other, with a fluid filling the gap between the cylinders. The cylinders
can be turned individually or together in opposition to one another. The
rotation of the cylinders produces lateral pressure gradients across the
fluid. The coherent patterns formed in these apparatuses is another example
of a gradient that produces macroscopic patterns from coherent microscopic
molecules. In this system the gradients are rotational pressure gradients,
not temperature gradients as in the case of Bénard cells.
An experiment showing the nonuniqueness of Taylor vortex flow. All three apparatuses
are the exact same size and have the same working fluids and the same rotation
rates, but show differing numbers of vortex pairs. Cylinder set A has thirty-two
vortex pairs, and the column rotation was initiated with a sudden jerk. Cylinder
set B has twenty-four vortex pairs and was started with a quasi-steady increase
in rotation rate. Set C has twenty-one vortex pairs and was started while the
fluid was filling the cylinders. Differing initial conditions control the final
states of the systems. Intense dark lines mark vortex sinks, and the weak dark
lines mark the location of radial outward motion. (Photograph courtesy of L.
Koschmieder.)
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