Re: Electric Current "Turbulence"

[William Beaty <billb@ESKIMO.COM>]

On Fri, 22 Oct 1999, Ed Schweber wrote:

>     We have a complicated schedule and it would be too much of a tangent to
> explain why I am teaching circuits in October. But yesterday a student asked
> me why there wasn't turbulence when two branches of a parallel circuit meet
> again. She didn't use the word "turbulence" but when I asked her if she was
> thinking about what might happen when two rivers merge, she said yes.
>
>    I have never heard of electric current turbulence but now that the
> question was posed I can't think of any reason why it shouldn't exist.


Heh!  I always wondered about this one myself.  For example, what happens
when electric charges flow from a narrow filament into a large-diameter
wire?  Isn't there a turbulent "jet" of charge flowing in the large wire?
Or when they flow from a large wire and into a narrow filament, could a
"charge tornado" appear in the large wire where charges spiral into the
mouth of the narrow filament?  I finally discovered the answer by asking
some questions: what is the time-constant of current loops in a copper
block?  Or, a similar question:  what force would be required to move all
of the electrons in a circuit at a drift velocity of many cm per second?

The answer is that all non-driven charge-flows in a copper block will
cease within a tiny fraction of a second.  If a copper block is vaguely
like a tank full of charge-stuff, the charge behaves more like cold tar
than like water.  It only moves when pushed, and when the pushing ceases,
the flow ceases instantly.  Also, the mechanical force required to produce
a large drift-velocity in a closed circuit is enormous, and as a result
the metal would immediately glow red hot from the work being expended
against the electrical resistance of the wire.  (And if we tried to pump
some thick paste through a long narrow pipe, immense pressure would be
needed, and the paste could heat the pipe red hot.)

The charge-sea inside of wires is a bit like a fluid, but it has a low
mass, and it experiences an immense amount of "friction" against the metal
lattice.  It is not quite right to imagine that wires are like
water-filled pipes.  Instead they are like pipes filled with fine wet
sand!  The "water" can be made to ooze along quite slowly through the
"sand," and waves of pressure can rapidly propagate through the sealed
pipes, but large-scale turbulence is damped out so fast that it is not
seen.

On the other hand, for high-frequency currents in microscopic conductors,
I think that a form of "turbulence" does exist.  Where turbulence arises,
we will see Chaos effects.  I've heard that Chaos appears in semiconductor
physics, and such things as "electron trajectory"  transistors and "Gunn
Diode" microwave oscillators can exhibit a kind of "electrical turbulence"
which produces Chaos.  The free charges in semiconductors behave more like
a gas than like a fluid, and they don't interact so much with the solid
lattice as they do in a metal.  However, any "turbulence" in electrical
currents is dominated by electromagnetic coupling, so it resembles
turbulence in plasma rather than in an everyday fluid.  Think about
Tokamak instabilities and solar prominences, rather than vorticies in a
bucket of water.


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