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Re: [Phys-l] Coriolis effect puzzlement



To emphasize the differences between spin/angular momentum calculated about
the earth’s axis vs spin/angular momentum calculated about a real or
gedanken arbitrary space pont (at which a future low pressure center might
form), consider two air masses located on the same meridian, a meter or so
apart apart. In an inertial frame, each has an Easterly directed velocity,
due to their partaking of the earth’s spin. Their angular momenta relative
to any point on the earth’s axis are in the same direction and completely
additive. In contrast, their momenta relative to a gedanken point midway
between them (and on their common meridian) are opposed in direction. The
question is, what happens if a low pressure center develops at the midpoint,
causing the air masses to move toward that midpoint. The proposed models
leading to a localized vortex seem to sidestep these complications.


From: John Denker
Sent: Friday, December 02, 2011 8:18 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Coriolis effect puzzlement
On 12/02/2011 03:50 AM, Bob Sciamanda wrote:
John Denker wrote:

“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.”
****************************************************
There seems to be a lacuna in this chain of reasoning:
How does spin of an air mass about the earth’s axis, stated in (2),
become
spin about a low pressure center, presumed in (4) ?
There is lacking a mechanism for STARTING THE SPIN ABOUT THE LOW PRESSURE
CENTER. In the rotating frame this is provided by the Coriolis effect.
What is the dynamical mechanism as viewed from an inertial frame?

The dynamical mechanism is called "friction", as explicitly
mentioned in item (2).

Again the rule is you can pick any reference frame you like,
but you can't mix-and-mismatch. Since you asked me to use
an inertial reference frame, don't be surprised if I use an
inertial reference frame.
-- In this frame, the air was spinning before the low
pressure center formed. Explanation: friction.
-- Immediately after the low pressure formed, it is
still spinning. Explanation: conservation of angular
momentum. Also friction.
-- At this point, maybe the air is at rest relative to
some rotating reference frame, but that is totally
irrelevant, because we are not using that frame. We
are not measuring rotation relative to whatever the
low pressure center is doing. The center is an abstract
point anyway, with zero size, so we can't even tell
whether or not the "center" is spinning. Again: you
asked me to use an inertial reference frame, so don't
be surprised if I rigorously stick to using an inertial
reference frame. In this frame, the air is spinning.
-- Immediately after the air fell in toward the center,
that part of the air is spinning faster than before.
Explanation: local conservation of angular momentum.

I don't see anything tricky about it. If you still think
there is something missing, please clarify the question.
_______________________________________________
Forum for Physics Educators
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Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/