Re: Hot air rising and automobile thermometers

[Leigh Palmer <palmer@SFU.CA>]

I'm sorry to have to post such a messy document, but it's getting
near my bedtime and I want to answer Herb's questions.

At 19:37 -0700 7/26/99, Herbert H Gottlieb wrote:
> On Mon, 26 Jul 1999 17:09:22 -0700 Leigh Palmer <palmer@SFU.CA> writes:
> > > But Leigh, surely a steady wind experiences more than one force.
> > > While the
> > > net-force should be zero, the current question really addresses the
> > > 'driving' force, the one that keeps the air moving in spite of the
> > > 'frictional-type' forces which must also be present.  Indeed, if
> > > there were no such driving force the motion of the air would soon
> cease.
> > There is more than one force acting, but there is no frictional
> > force. Given a piece of air in a steady wind the immediately adjacent
> air is
> > moving at the same speed. By "to first order" I mean considering no
> > wind shear. The conventional explanation of geostrophic winds is of
> > first order. In this case the net force is zero. The force due to the
> > horizontal component of the pressure gradient is exactly balanced by
> > the horizontal component of the Coriolis force. Of course more forces
> > are present in real situations, but those are the two large forces.
> >
> > When you have internalized this idea you will be one step farther
> > from the seductive Aristotelean construct, that force impels motion,
> > which seems to follow us around for years after we learn that it is
> > fundamentally incorrect. I have the same problem.
> >
> > Leigh
>
> It would really be appreciated if you would rephrase your
> explanations a  little to help me (and possibly some others)
> clarify the basic concepts that are involved in your discussion
> in this thread concerning winds and air currents.
>
> 1. Most earth science and meteorology textbooks refer to
> "wind" as a horizontal movement of air, either close to the
> earth or aloft.  What do you mean by calling wind a "horizontal
> component of a pressure gradient"?

I didn't do that. I merely note in passing that there is always
a vertical pressure gradient in the atmosphere; wind (horizontal
movement of air) is associated only with horizontal pressure
gradients.

> 2. If a force "due to the horizontal component of the pressure
> gradient is exactly balanced by the horizontal component of
> the Coriolis force" what causes the Coriolis acceleration ?

There is no Coriolis acceleration to this order because there
is an equal, opposite force acting on the moving air.

> 3. If, as you say, there is no frictional force to stop the
> movement of air once it is in motion,  why doesn't
> the wind continue blowing forever once it has been
> started by a pressure gradient?

I didn't say that there are no frictional forces. I said that
such forces are unimportant because they are absent in the case
where there is no wind shear (constant velocity wind over
spatial dimensions). I suppose I suppose the wind would blow
forever if the pressure gradients did not vary in time. They do
vary, of course.

I thought this mechanism to be well understood in this group.
Do we not tell our students that air circulates counterclockwise
around a low pressure center in the northern hemisphere (called
a "cyclone")? This circular motion is the next order up from the
geostrophic wind. The pressure gradient force is very slightly
greater than the Coriolis force, and circular motion is the
consequence, to second order in the forces.

Finally a religious comment: I simply cannot understand why so
many physics teachers still object to use of centrifugal force
and Coriolis force to explain physical phenomena in rotating
coordinate systems. We live in a noninertial system. Gravity and
rotation are ubiquitous. How can we deprive our students of such
readily accessible tools for understanding, apparently solely on
religious grounds? The phenomena of winds, cyclones, and many
others become less mysterious when these forces are appreciated.

Leigh