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Re: [Phys-L] Coriolis effect



Thanks for the detailed reply. The diagrams online usually show winds
heading toward the equator in both hemispheres deflecting to the west and
winds heading away from the equator (toward the poles) deflecting to the
east. So then, using basic physics language, how do we get hurricanes in
each hemisphere spinning in opposite directions?

On Fri, Oct 22, 2021 at 1:15 PM John Denker via Phys-l <
phys-l@mail.phys-l.org> wrote:

On 10/22/21 9:20 AM, Anthony Lapinski wrote:

Some of the information/diagrams were
confusing/contradictory - right, left, eastward, westward, etc. Did not
fully explain how the spin happens.

Agreed. There is a very high prevalence of utter garbage
on this topic. That includes some stuff that's off by
a factor of 2, due to including half of the physics but
not all.

Book says hurricanes spin CCW in the northern hemisphere and CW in
the southern hemisphere. True, but why?

The simplest qualitative answer proceeds as follows:

1) There is no "relativity" principle for rotation. That is
to say, a rotating reference frame is not the same as a
non-rotating reference frame.

Everybody on this list knows this, but students need to be
reminded more than once.

2) An air mass that appears stationary on the weather map is
rotating ... because the map itself is rotating (except right
at the equator).

3) A cyclone is a low-pressure system. That means low pressure
at the surface. In the absence of rotation, air would rush
inward to "fill in" the low.

In case you were worried about conservation of air molecules:
There is low pressure at the surface because the air went
/up/. Rising air creates low pressure /at the surface/.
So in the absence of rotation, the picture would be inflow
(toward the center) at the surface, upflow at the center,
and outflow aloft.

4a) Angular momentum is conserved. It's like the proverbial ice
skater pulling her arms and legs inward. When air flows inward
toward the center of a cyclone, the rate of rotation (relative
to absolute space) increases. It is now rotating faster than
the map, so it is seen to rotate relative to the map.

Very soon the force associated with the rotational flow field
cancels the pressure gradient, so you get dynamic equilibrium,
with velocity /perpendicular/ to the pressure gradient.

Students find it highly counterintuitive to see the motion be
perpendicular to the applied net force. They are accustomed to
seeing things move in the direction they push them.

This is a qualitative answer. It is 100% true as far as it goes.
It is sufficient for many purposes. It has the remarkable property
of being /independent of mechanism/. It does not explain "how" the
air speeds up, but it guarantees that it /will/ speed up.

To quantify the steady-state situation, the easiest thing is to
make a further change of reference frame. Choose a frame corotating
with the air mass (not with the map). In this frame, there is no
Corolis effect, just centrifugal force.

This is a quantitative answer. It is good enough for almost all
practical purposes. Even so, it doesn't explain the mechanism that
created the steady-state flow pattern.

====

If you want to understand the transient /mechanism/ )including
the Coriolis effect, as mentioned in the Subject: line) you need
to re-express the equations of motion in the rotating frame. This
requires little more than the chain rule for differentiating a
function of a function.

==

If you want to /visualize/ what's going on, you have to be careful.
A lot of people manage to notice the first term in the answer and
overlook the second ... or vice versa. Hence the prevalence of
answers that are wrong by a factor of 2.

The lurid details, including diagrams, are here:
https://www.av8n.com/physics/rotating-frame.htm
_______________________________________________
Forum for Physics Educators
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