Re: [Phys-L] conserved momentum thru gas...

[John Denker <jsd@av8n.com>]

On 12/21/22 1:32 PM, O A via Phys-l wrote:

> Interestingly, the "how" became important for me precisely when regarding
> the "steady state".
>
> It isn't uniform in this, right?

I said /in the absence of disturbances/, the steady state
is uniform.

The two parts of that sentence go together.
Don't take the second part out of context.

> I'm not sure how best to regard this as 1 single FoR when there must
> be some diffential in order to have the coriolis effect with respect to the
> atmosphere manifest.
> So: 2 separate FoR, the non inertial solid/liquid earth and its inertial
> atmosphere.

My advice: In this situation (and in *many* others):
Pick a single frame of reference and stick with it.

The frame is the frame.
The fluid is the fluid.
The frame need not be attached to the fluid.
Pick one overall well-behaved frame and stick with it.

Centrifugal terms appear in the equations of motion if and only
if the *frame* is rotating. Coriolis terms arise if and only if
the fluid is moving relative to the rotating frame.

Let's be clear: If you analyze a rotating fluid using a
non-rotating reference frame, there are no centrifugal or
Coriolis forces.

For the next level of detail, here's a fairly simple no-BS
discussion (including derivation) of the laws of motion in
a rotating frame:
  https://www.av8n.com/physics/rotating-frame.htm

Beware that there are a great many BS discussions floating
around on the web. In particular, hand-wavy derivations
commonly get the magnitude of the Coriolis term wrong by
a factor of 2.

> inertial solid/liquid earth and its inertial atmosphere
The word "inertial" means different things to different
people, but no matter what it means in this context, there
is nothing to be gained by considering the atmosphere more
inertial or less inertial than the earth. Forsooth, I would
argue that's not even the right question; it would be better
to ask whether the *frame* is inertial.

In any case, again I recommend picking one overall
reference frame and sticking with it. In this context it's
traditional and reasonable to pick a frame corotating with
the solid earth. This is the frame used for navigation and
for maps of all kinds, including weather maps. I would
label this frame as non-inertial since it is rotating.
Again: Centrifugal terms arise if and only if the *frame*
is rotating. Coriolis terms arise if and only if the thing
of interest is moving relative to the rotating frame.

  Note: The aforementioned frame is often call the "lab"
  frame. It is sometimes called an inertial frame, although
  this is only an approximation, as you can demonstrate
  with a Foucault pendulum. The centrifugal and Coriolis
  terms are far more significant on planetary size-scales
  and time-scales than they are on laboratory scales.