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Re: [Phys-l] Coriolis effect puzzlement



On 12/01/2011 03:53 PM, Bob Sciamanda wrote:
The problem which I then propose to your expertise is to analyze and
mathematically model the behavior of the earth’s atmosphere in the
neighborhood of a pressure high/low, AS OBSERVED FROM AN INERTIAL FRAME.
Hopefully this model will show the true dynamical origin of the
configurations cited in airplane pictures as Coriolis efects.

OK

I realize that this is probably an impossible task, but I trust that your
investigation will at least show some directions towards a plausible model.

It's not impossible. It's not even hard.

1) Relative to the inertial frame, the earth is observed
to spin.

2) Due to friction, we are not surprised to find that
on average, the atmosphere spins along with the solid
earth. We take this as a zeroth-order approximation
to the actual behavior.

3) There are various local effects such as uneven solar
heating, orography, precipitation (which liberates a
lot of latent heat), et cetera. Sometimes these result
in a local updraft. This leaves us with a local low
pressure area.

4) As the rotating air mass falls into the low pressure
area, the rate of spin increases. This can be explained
in terms of conservation of angular momentum. It can
equally well be explained in terms of conservation of
linear momentum, in accordance with Newton's third law,
if you want to do things the hard way.

5) This suffices to explain, to first order, the structure
of a vortex such as a dust devil, tornado, or hurricane.
Since we analyzed it using an inertial frame, there are
no centrifugal fields and no Coriolis effects.

6) There are additional second-order corrections, such as
friction of a given air parcel against another, or against
the ground. This explains why the "arms" of a hurricane
are spirals rather than perfect circles.