What Does the Coriolis Effect Really Refer To?

[pwn01]

Does the term "Coriolis effect" refer to the phenomenon that causes the sheering of wind (or other objects) due to the difference in angular velocity encountered when moving from north to south or south to north, or . . .

does it refer to the turning observed with a Foucault pendulum that is caused by the rotation of the earth?

 

[jfizzix]

The Coriolis effect is the effect which drives the Foucault pendulum, and which drives cyclones to be counter-clockwise in the northern hemisphere and clockwise in the southern hemisphere.

In particular, the Coriolis force is a "ficticious force" that is due to being in a rotating (accelerating) reference frame (in this case the surface of the spinning Earth). It's proportional to your velocity, but always perpendicular to it. It is also perpendicular to the axis of the spinning object.

For all horizontal motion in the northern hemisphere, the Coriolis force is always in the direction 90 degrees to the right of the velocity. The Foucault pendulum knocks down a circle of dominoes in clockwise order for that reason.

Mathematically,
$\vec{F}_{coriolis} = 2m \;\vec{v}\times \vec{\omega}$
where $\vec{v}$ is your velocity, $\vec{\omega}$ is the angular velocity of the Earth with direction pointing out the north pole, and $m$ is your mass. The "$\times$" is a vector cross product.

 

[pwn01]

Just to make sure that I understand cyclones. In the northern hemisphere, cyclones rotate counter-clockwise because the pressure gradient balances with the Coriolis force.

A Foucault pendulum is subject only to the unbalanced Coriolis force and so rotates clockwise in an inertia circle.

 

[jfizzix]

In the northern hemisphere, northerly moving air is deflected to the east, and southerly moving air is deflected to the west. Because cyclones have a low pressure zone in their center, moving air (that would otherwise equalize that pressure) is at once deflected away from the center by the Coriolis force (keeping the low pressure zone low), and pulled toward it due to the fact that it is a low pressure zone. The Coriolis force also drives circular airflow around high pressure zones too (these are called anticyclones), but these weather systems are not as dramatic because the Coriolis force and the pressure gradient force don't oppose one another; they both work to dissipate the anticyclone. (you will want to check this out for yourself as I am not an expert in atmospheric physics)

A Foucault pendulum is actually subject to the centrifugal force in addition to the Coriolis force, though the centrifugal force due to the spinning Earth is rather small, and is easily accounted for by slightly adjusting the "constant" value of the acceleration due to gravity. The Coriolis force is exclusively responsible for changing the direction a Foucault pendulum swings in over time.

 

[pwn01]

Thanks for your reply. I'm needing to delineate in my mind the forces acting on wind (or objects) moving across the Earth's surface. I started another thread titled "Conservation of angular momentum" which, by the response I received, maybe should be titled "Conservation of linear momentum." Maybe also the two threads should be combined.

Another questions:

Is it safe to say that the Coriolis force is not accurately portrayed with the frictionless spinning disk and ball rolling from the center to the edge? What it appears to me is that the ball would never follow an inertia circle with that setup. No matter how large the disk, nor how slowly the ball rolled, it would simply spiral to the edge of the disk and fall off. To illustrate it, you would have to have the ball basically moving with the disk except for its independent velocity that gives it inertia within the whole system. The inertia of the ball would tend to keep it pointing in the same direction relative to a point outside of the disk. This would force it to have to pivot on the surface of the disk (as the disk rotated) to maintain its desired direction. This pivoting would cause it to form an inertia circle on the disk. The "force" that causes this circling is properly called the Coriolis "force." Correct?

 

[pwn01]

Here is a quote from the article that I cited in the other thread.

"Some textbooks (and educational sites on the
World Wide Web) explain qualitatively the Coriolis
deflection of a meridional movement as a consequence
of the air’s origin at another latitude where its velocity
due to the earth’s rotation was different (e.g., Battan
1984, 117–118). But this does not relate to the principle
of conservation of angular momentum, but to
conservation of absolute velocity. This misunderstanding
is deceptive because it yields a deflection in the
right direction, but only explains half of the Coriolis
acceleration ω × v_r instead of 2 ω × v_r. The seriousness
of the mistake lies not primarily in the numerical
error, but in the confusion between two fundamental
mechanical principles: conservation of linear momentum
and conservation of angular momentum. This potential
misunderstanding is acknowledged by Eliassen
and Pedersen (1977, 98), who make it clear how two
kinematic effects each contribute half of the Coriolis
acceleration: relative velocity and the turning of the
frame of reference. This can also be understood from
simple kinematic considerations (Fig. 3)."

Citation: http://www.aos.princeton.edu/WWWPUBLIC/gkv/history/Persson98.pdf, page. 4 (1376).

This seems to indicate that both the rotation of the frame of reference and the conservation of "absolute velocity" contribute to the total Coriolis effect.