Re: [Phys-l] Coriolis effect puzzlement

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

I just want to point out one thing that some people seem to be glossing
over here: on the non-inertial frame of the rotating earth, the
centrifugal effect is *not* observed because, for the Earth, the
centrifugal effect is balanced by a *centripetal* force.  Otherwise,
objects at rest relative to the surface would accelerate toward the
equator.  Basically, we define horizontal such that that the normal
force is not strictly radial but has a centripetal component (in a
sense).  This is why we can focus only on the Coriolis effect.  That is
why, if the Earth was perfectly smooth (but not a perfect sphere), a
ball rolled from the north pole would not reach the equator.

By the way, JD's 1-4 is essentially the logic I recommend teachers use
for students (as I suggested to Anthony in my previous note).  Don't
even mention Coriolis, as that just complicates things.  Besides, you
can use 1-4 to explain everything we need to explain, including why it
is unlikely for a hurricane to rotate opposite the rotation of the Earth
-- its size.  The initial ambient flow would have to be significant in
order to have an *initial* rotation opposite the Earth's.  This is more
likely for an area the size of a tornado's inflow region.  For an area
the size of a sink, it doesn't take much to make the initial rotation
direction on way or the other.

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Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@esu.edu    http://www.esu.edu/~bbq 


-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John
Denker
Sent: Thursday, December 01, 2011 6:12 PM
To: Forum for Physics Educators
Subject: 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.