Re: [Phys-L] Coriolis effect

[John Denker <jsd@av8n.com>]

On 10/22/21 12:11 PM, Anthony Lapinski wrote:

> The diagrams online usually show

As Feynman put it: I'm not responsible for what other people say.

Also:  https://m.xkcd.com/386/

Also: Nie mój cyrk, nie moje małpy.

> 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?

Perhaps I'm not understanding the question. For 99% of the
applications the conservation-based answer (as previously
discussed) is the right way to go. The air was rotating before
the cyclone formed, because the whole planet is rotating. After
the cyclone forms, the air is still rotating, only faster. It
has the same angular momentum in a smaller area, so it rotates
faster.

Opposite hemispheres rotate in opposite directions, so the
cyclones rotate in opposite directions. You will never get
a question with a simpler answer. Conservation of angular
momentum.

======================

If you insist on a Coriolis answer, we can do that too, but
it's more complicated.

Mentioning (even briefly) the equator is asking for trouble.
The effect is not observed near the equator.

Let's restrict the discussion to northern§ temperate latitudes.
Viewed from above, the whole scene is rotating CCW§ relative
to absolute (non-rotating) space.
(Words marked § need to be reversed in the other hemisphere.)
An air mass that appears stationary relative to the weather
map is rotating, because the map itself is rotating. The whole
planet is rotating. It is customary to use this rotating
reference frame.

Coriolis and centrifugal effects exist in the rotating frame
and not otherwise.

Let's start with equilibrium, such that a static pressure gradient
cancels centrifugal force. So all that remains is Coriolis.

The short, smart way to express it is to say that any parcel of
air moving relative to the map will bend to the right§.

  It's true (but less clever) to say that a parcel of air moving
  northward§ relative to the map will bend to the right§ (westward)
  and a parcel flowing southward§ will also bend to the right§
  (eastward).

  Meanwhile, it is equally true (but less commonly mentioned) that
  a parcel flowing eastward or westward relative to the map will
  also bend to the right§. Everything bends to the right§.

A cyclone is a low-pressure region. The brief initial tendency is
for air to flow inward to "fill in" the low. As it does so, it
veers to the right§. So before long we have a lot of air flowing
CCW§ around the low.

After the brief initial transient there is enough air flowing CCW§
around the low so that centrifugal force (in the new frame comoving
with that air) cancels the inward pressure gradient. This is the
steady state. This is the observation that we were asked to explain.

  In the much longer term, friction will mess things up and allow
  some longer-term inward flow, but that's the answer to a different
  question.

The above is the Coriolis answer. It's a valid answer, but the
conservation answer is much simpler and more elegant.