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Re: [Phys-l] Coriolis effect puzzlement



On 12/01/2011 11:55 AM, Bob Sciamanda asked:

Why is the Coriolis effect observed in pictures taken from airplanes? Is
the airplane camera in a rotating frame?

I refer, for example, to Figure 12 of
http://en.wikipedia.org/wiki/Coriolis_effect.

The short answer is that the Coriolis effect is real physics,
and will be observed from airplanes *or anything else* if you
look carefully.

Another answer is that you need an airplane (or more likely
a satellite) to get high enough to see the overall shape of
a hurricane at one glance. OTOH you could have pieced
together more-or-less the same picture by combining lots
of ground-based observations. By the same token, anybody
can see at a glance the rotation of a smaller storm such
as a tornado, with no need for spacecraft or anything else.

Certainly the Coriolis effect has got nothing to do with the
rotation of the airplane or the camera.

As always, the relevant rotation rate is the rotation of the
/reference frame/ ... and in this case we choose a frame
corotating with the earth.
-- The relevant rotation rate is not the rotation of the
airplane or camera.
-- It is also not the rotation rate of the storm. We are
not analyzing the situation in a frame corotating with the
storm (although I suppose we could if we wanted).

There's a pedagogical question as to why anyone would use figure
12 to illustrate the Coriolis effect. The caption mentions
counterclockwise motion and mentions the pressure gradient, but
you can't see either one of those things by looking at the picture.
Without lots of additional information, you have no idea what the
velocity is or what the pressure gradient is.

In the steady state, very little of the structure of the hurricane
is explained by the Coriolis effect. In particular, some small
percentage of tornadoes in the northern hemisphere spin the "wrong"
way i.e. clockwise, and they don't look any different. In the
steady state, most of the deflection of the air parcels, as they
go around the center of the storm, is explained by the pressure
gradient, without mentioning Coriolis.

As an /initial/ value problem, you can use Coriolis to explain
where the /initial/ spin came from ... but figure 12 doesn't
allow us to watch the initialization.

The cloud rotation does not seem to be merely “relative to the ground” – the
ground isn’t even visible.

Visibility has got nothing to do with it. As always, the rule
is simple: The Coriolis effect exists in the rotating frame
and not otherwise.

Let's assume we're in the northern hemisphere.

The point is that in the situation we refer to as "calm winds",
when the weather map is showing no wind, the air mass is
rotating, because the map itself is rotating! It partakes of
the rotation of the earth.

Now, if you have a parcel of air that is moving relative to
the map, it will not move in a straight line relative to the
map. According to the free-particle equations of motion in
the rotating frame, it will get deflected to the right.

Of course it will also get deflected by any unbalanced forces,
such as the pressure gradient.

Perhaps the effect is due to the fact that, even as seen from space, the low
pressure center is tied to a rotating earth.

The low pressure center is not "tied" in any significant way
... and tying it wouldn't affect the Coriolis issue.

The point is, as always: the centrifugal field exists in the
rotating frame and not otherwise.

We could choose to analyze things in a non-rotating frame,
in which case the Coriolis effect would go away! The
physics would be the same, and the satellite photo would
be the same, but the words used to describe it would be
different. This is important. The Coriolis effect exists
if and only if the /reference frame/ is rotating.

The reference frame may or may not be tied to any particular
object.

Again: *IF* we choose to analyze things in a rotating frame,
there will be Coriolis effects, in proportion to the rotation
rate of the reference frame, multiplied by the velocity of
the object relative to the rotating frame.

On 12/01/2011 12:50 PM, Bennett wrote:
Why has no one mentioned the vertical component of airflow?

For the same reason they have not mentioned friction of the
air parcels against each other, and against the ground.

Vertical motion plays a major role in setting up the low
pressure region in the middle of a storm.

Thereafter, if we neglect vertical motion and neglect friction,
the big vortex structure is stable, and would last forever.
It is a good strategy to analyze this simplified system, and
then add in friction and vertical motion etc. as relatively
small perturbations.